“Green Jade” is a vegetarian dish of broccoli, string beans and snow peas. When chicken is added, the dish becomes “Green Jade Chicken.”
   
“Green Jade Chicken Szechuan Style—slice white meat chicken, sauteed with house special sauce, surrounded with broccoli” was printed in the Dallas (TX) Morning News on July 17, 1977. “Chicken with broccoli (creatively listed as green jade chicken)” was printed in the Texas Monthly in February 1978.

Another “Green Jade” dish is “Green Jade Scallops.”
 
         
17 July 1977, Dallas (TX) Morning News, “Szechuan Chinese Restaurant stimulating to the palate,” pg. 16B, col. 7:
(Szechuan Chinese Restaurant, 4117 Lemmon Avenue between Douglas and Knight.—ed.)
Green Jade Chicken Szechuan Style—slice white meat chicken, sauteed with house special sauce, surrounded with broccoli.
 
Google Books
February 1978, Texas Monthly, “Dining Out” by W.L. Taitte, g. 122, col. 2:
Even the bland dishes can be rewarding, like chicken with broccoli (creatively listed as green jade chicken), though these dishes tend to be oilier than American sensibilities might prefer.
 
25 January 1979, The Pantagraph (Bloomington-Normal, IL), pg. B-6, col. 1 ad:
green jade chicken
(Peking Palace, Landmark Mall.—ed.)
 
24 April 1981, Florida Today (Cocoa, FL), “Hoo Nan unveils Easter changes” by Carolyn Short, pg. 1B, col. 1:
(Hoo Nan Chinese Restaurant, 666 U.S. 1.—ed.)
... green jade chicken, green jade scallops, ...
     
12 February 1982, Omaha (NE) World-Herald, pg. 18, col. 1 ad:
Green Jade Chicken
(Hunan Garden, 60th & Center.—ed.)
 
26 April 1987, Newsday (Long Island, NY), “Dining Out” with Peter M. Gianotti, Magazine sec., pg. 37, col. 2:
(Dragon Gate, 308 Main Street, Huntington.—ed.)
Dragon Gate’s “green jade chicken” is short on the advertised ginger, but is a glistening saute swathed with stringbeans.
 
20 February 2003, Ithaca (NY) Journal, Spring Dining Guide sec., pg. 23, col. 1:
GREEN JADE CHICKEN
Sliced chicken, string beans, snow peas, broccoli, straw mushrooms ... $8.25
(Hong Kong Chinese Food, 120 Dryden Road, Collegetown, Ithaca, NY.—ed.)
 
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Empire Schezuan Green Jade Chicken! RT @Third_Watch Bosco: Good, I got a date with a Chinese chicken. #thirdwatch
8:02 PM - 18 Oct 2012