“Oysters Rockefeller” (also called “Huitres en Coquille a la Rockefeller” and “Huitres, a la Rockefeller” was invented at Antoine’s Restaurant in New Orleans, Louisiana, by proprietor Roy Alciatore (grandson of the original owner). The dish is rich, and John D. Rockefeller (1839-1937) was one of the wealthiest persons in the United States in the early 1900s.
 
It is not known when Oysters Rockefeller was invented—the year is often given as 1889 or 1899—but Antoine’s advertised “Something new at Antoine’s...Huitres, a la Rockefeller” in the The Times-Democrat (New Orleans, LA) on October 24, 1909.
 
A recipe was published in the Chicago (IL) Daily Tribune on March 26, 1912:
 
“Huitres en Coquille a la Rockefeller—Raw oysters with a dressing made as follows, the quantity of the ingredients depends of the size of the order: One bunch of shallots, one bunch of parsley, two pounds of butter, one bottle of Spanish walnuts, half a bunch of tarragon leaves, two stale loaves of French bread, salt and pepper, and a liberal sprinkling of tabasco sauce. All of these things are pounded into a pulp in a mortar and then ground in a sausage machine, the mass being finally passed through a needle sifter. The oysters on the half shell are covered with the sauce and then placed in a hot oven to bake just three minutes. The oysters must be served at once.”
       
         
Wikipedia: Oysters Rockefeller
Oysters Rockefeller is an oyster dish created at the New Orleans institution Antoine’s. Jules Alciatore adapted a similar recipe to use oysters instead of snails during a shortage of French snails and diners’ declining taste for them. Antoine’s founder Antoine Alciatore created the original snail recipe. Though many New Orleans restaurants serve dishes purporting to be Oysters Rockefeller, the owners of Antoine’s claim that no other restaurant has been able to successfully duplicate the recipe.
(...)
However, Antoine’s chefs have repeatedly denied that the authentic recipe contains spinach. Since 1899, Antoine’s and other fine French/Creole restaurants have been making this rich oyster dish, a combination of oysters, capers, parsley, and parmesan cheese, topped with a rich white sauce of butter, flour, milk, etc.
 
As the dish is so rich, it was named for the richest American of the time, John D. Rockefeller. 
 
Wikipedia: John D. Rockefeller
John Davison Rockefeller, Sr. (July 8, 1839 – May 23, 1937) was an American industrialist who played a prominent role in the early oil industry with the founding of Standard Oil (ExxonMobil is the largest of its descendants). Over a forty-year period, Rockefeller built Standard Oil into the largest company in the world, and was for a time the richest man in the world.
 
Wikipedia: Antoine’s
Antoine’s is a Louisiana Creole cuisine restaurant located at 713 rue St. Louis (St. Louis Street) in the French Quarter of New Orleans, Louisiana. It has the distinction of being one of the oldest family-run restaurants in the United States, having been established in 1840 by Antoine Alciatore. A New Orleans institution, it is notable for being the birthplace of several famous dishes, such as Oysters Rockefeller, Pompano en Papillote, Eggs Sardou and Pigeonneaux Paradis
       
Antoine’s Restaurant
History of Antoine’s
Established in 1840, Antoine’s is the country’s oldest family-run restaurant.
(...)
After Antoine’s death, his son Jules served as apprentice under his mother’s tutelage for six years before she sent him to France where he served in the great kitchens of Paris, Strassburg and Marseilles. He returned to New Orleans and became chef of the famous Pickwick Club in 1887 before his mother summoned him to head the house of Antoine.
 
His genius was in the kitchen where he invented Oysters Rockefeller, so named for the richness of the sauce. They remain one of the great culinary creations of all time and that recipe remains a closely-guarded Antoine’s secret, though it has been imitated countless times.
 
24 October 1909, The Times-Democrat (New Orleans, LA), pg. 15, col. 7 ad:
Something new at Antoine’s
Huitres, a la Rockefeller.
(...)
Open After the Opera
ANTOINE’S
713-717 St. Louis Street
 
25 September 1910, Kansas City (MO) Star, pg. 10C, col. 6:
SEE ANTOINE’S AND LIVE.
If in New Orleans Drive Over the Rough Cobble Stones to the Ecstacy of Dining.
It was on the other side of Canal Street. Four blocks down Royal Street, where the old architecture of France and the new architecture of the courthouse meet—drive half a block over the rough cobble stones brought from France years ago, and you are there. Antoine’s! You have heard of Antoine’s. Everybody who has heard of New Orleans has been told of Antoine’s. It is famous; it desire to be.
 
Out of a most elaborate and high sounding French menu you would easily pass Canape Roosevelt, and it would be to sneer at Oysters Rockefeller, but after you put yourself in the hands of a suave and really clever waiter, who rattles off everything in French so fast you wouldn’t recognize the President’s name—you feel relieved and prepare for his “nice little dinner.” Your oysters are Rockefeller, served with a great air, but they might be Napoleon or Bismarck, or Carnegie, or Martin Reagan, for all you care—for they really are Antoine’s. Such oysters! You half guess they are a bit baked with much parsley—an undefinable charm that has grown to mean garlic down here hovers over them and they float about in the shell in a nectar that—but why try to tell you—it’s just oysters Antoine—like nothing you ever tasted before.
 
19 March 1912, Chicago (IL) Daily Tribune, “Economical Housekeeping: The Gulf Oyster” by Jane Eddington, pg. 8:
Once in New Orleans we hasten for our first luncheon to Restaurant de la Louisiane—the Louisiane for short—and there we find that we can have oysters Rockefeller, oysters Louisiane, oysters brochette, oysters marieniere, oysters on the half shell, fried oysters, and, of course, oyster cocktail.
(...)
Oysters Rockefeller—We forgot to ask Louis why the name, but when you see what condensed richness is put into the dressing of half a dozen roasted oysters, served on the half shell, you can answer why for yourself. To begin with the oysters, on the shell, resting on a bed of rock salt, are roasted for five minutes under the fire in a fireplace—in the oven it would take seven or eight minutes to roastthem. The sauce: This is made of a number of greens ground in a sausage grinder—this is what Louis calls the meat grinder—pounded with a little butter, to which is added one teaspoon of essence of anchovy, a few drops of tabasco sauce and the same of Worcestershire sauce. The greens are tops of shallots—more of them that anything else—a bit of cress, celery, parsley, spinach, chives amd chervil. This latter is rare and must be grown in hotbeds. It is so grown in gardens both quite far north as well as south. If this latter is not obtainable a few drops of absinthe is added to give the flavor of anist. One tablespoon of this sauce is dipped over each roasted oyster—oyster Rockefeller as served at the Louisiane.
     
26 March 1912, Chicago (IL) Daily Tribune, “Economical Housekeeping: French Specialties” by Jane Eddington, pg. 6, col. 5:
New Orleans, March 25—(...) We had gone for dinner to the famous Antoine’s.
(...)
We had oysters Rockefeller elsewhere, but the only recipes we brought away were the one we had for this and one for the soup we had. These were the only ones printed on the great sheet, giving a history of the house, which we received as a souvenir. The last section of this begins:
 
“Monsieur Jules has invented many dishes which have added to the name of his house, chief among them being huitres en coquille a la Rockefeller. ROckefeller’s name suggests that golden flavor, that’s why it was added to the huitres.
(...)
“Jules is extremely reluctant about giving away the secrets of his kitchen, but after some coaxing he was induced to part with the following while slowly sipping cognac after luncheon:
 
“Huitres en Coquille a la Rockefeller—Raw oysters with a dressing made as follows, the quantity of the ingredients depends of the size of the order: One bunch of shallots, one bunch of parsley, two pounds of butter, one bottle of Spanish walnuts, half a bunch of tarragon leaves, two stale loaves of French bread, salt and pepper, and a liberal sprinkling of tabasco sauce. All of these things are pounded into a pulp in a mortar and then ground in a sausage machine, the mass being finally passed through a needle sifter. The oysters on the half shell are covered with the sauce and then placed in a hot oven to bake just three minutes. The oysters must be served at once.”
 
Google Books
January 1914, Harper’s Bazar (New York, NY), “I beg your pardon Broadway” by Charles Belmont Davis, pg. 12, col. 1:
Where the New Orleans Atmosphere is Found
(...)
I will give the menu of the first lunch I ever ate at Antoine’s, because it is pretty sure to be the lunch that any waiter there will suggest to any tourist who enters the place for the first time:
 
Oysters Rockefeller
(or Canapé of Crab-meat) Gumbo
 
28 January 1916, Chicago (IL) Daily Tribune, “The Tribune Cook Book: New Orleans Oysters” edited by Jane Eddington, pg. 14, col. 7:
At both the Louisiane and Antoine’s they serve oysters Rockefeller. At the Louisiane they are roasted on the half shell under hot coals for five minutes and served with a green herb sauce. A bed of rock salt is used to set the shells on. At Antoine’s oysters a la Rockefeller were covered with the green sauce and roasted just three minutes in a hot oven.
 
Antoine’s Herb Sauce.
Tops of shallots, parsley, bits of cress, celery, chives, etc., are chopped and pounded together with butter to make these sauces which are often flavored with essence of anchovy, Worcestershire sauce, and sometimes bread crumbs.
     
15 January 1925, Dayton (OH) Daily News, “En Tour With O. O. by O. O. McIntyre, pg. 6, col. 3:
(The New York City columnist in New Orleans.—ed.)
They arrived near mid afternoon and we went to Antoine’s for lunch. We started off with their most famous dish—Oysters Rockefeller cooked in the hot sands as they are cooked in Castle Cave in New York.
   
13 September 1934, New York (NY) Times, pg. 23, col. 3:
JULES ALCIATORE, FAMOUS CHEF, DIES
Proprietor of Antoine’s in Now Orleans for 50 Years Devised Many Notable Dishes.
DELIGHTED 4 PRESIDENTS
Two of His Creations, Oysters Rockefeller and Care Brulo Diabolique, Widely Known.
 
Chronicling America
5 October 1937, The Evening Star (Washington, DC), “Shellfish May Be Used To Make Substantial And Tasty Dishes” by Betsy Caswell, pg. B-12, col. 5:
OYSTERS ROCKEFELLER.
1 small bunch raw spinach.
2 bunches Spring onions.
Leaves from three bunches celery.
1 head lettuce.
1 bunch parsley.
3/4 pound butter.
1 handful fine bread crumbs.
3 teaspoons Worcestershire sauce.
1 teaspoon anchovy sauce.
Oysters on half shell.
Chop the spinach, onions, celery leaves, lettuce and parsley very fine. Melt the butter and add it, with the bread crumbs, to the chopped herbs. Season and stir into a thick sauce. Spread this mixture over the oysters in their shells; set them in a shallow pan filled with ice cream salt to hold them in place and bake in a hot oven until brown. Serve very hot on plates filled with heated ice cream salt.
 
3 March 1957, New York (NY) Times, “Cooking in Creole—New Orleans Style” by Jane Nickerson, pg. 217:
To this must be added such typical cocktails as absinthe suisesse and Ramos gin fizz, the flaming coffee called cafe brulot and the various baked oysters that are variations on the oysters Rockefeller of Antoine’s restaurant.
 
Founded in 1840, Antoine’s is administered by Roy Alciatore, grandson of the original owner.