New York (NY) Times food journalist Craig Claiborne (1920-2000) wrote on November 16, 1967:
 
“The Adrian Zorgniottis agree with G. K. Chesterton, who told a friend, ‘Music with dinner is an insult both to the cook and violinist.’”
 
English author G. K. Chesterton (1874-1936) was famous for his sayings and proverbs. Claiborne wrote that Chesterton made the remark to Francis Robinson (1910–1980), one-time assistant manager and television host for the New York’s Metropolitan Opera. It’s not known when—or if— the remark was made. Chesterton died in 1936; Robinson joined the Metropolitan Opera in 1946. It’s probable that Claiborne knew Robinson and heard the remark from him, but that the credit to Chesterton was a mistake.
   
   
Wikipedia: G. K. Chesterton
Gilbert Keith Chesterton, KC*SG (29 May 1874 – 14 June 1936), better known as G. K. Chesterton, was an English writer, poet, philosopher, dramatist, journalist, orator, lay theologian, biographer, and literary and art critic. Chesterton is often referred to as the “prince of paradox.” Time magazine has observed of his writing style: “Whenever possible Chesterton made his points with popular sayings, proverbs, allegories—first carefully turning them inside out.”
 
16 November 1967, New York (NY) Times, “The Doctor Prescribes Music After Dinner, but Not With It” by Craig Claiborne, pg. 54, col. 1:
THE Adrian Zorgniottis agree with G. K. Chesterton, who told a friend, “Music with dinner is an insult both to the cook and violinist.” But after dinner, that’s another story.
(...) (Col. 2—ed.)
A recent guest at dinner included Marcia Davenport, the author and daughter of Alma Gluck, and Francis Robinson, assistant manager of the Metropolitan Opera. It was to Mr. Robinson that Mr. Chesterton made that remark about music with dinner.
 
22 June 1973, The Morning News (Wilmington, DE), “Cryptic Byword” by MAC, pg. 50, col. 2:
Music with dinner is an insult both to the cook and the violinist.—G. K. Chesterton
 
Google Books
An Encyclopedia of Quotations About Music
Compiled and edited by Nat Shapiro
New York, NY: Da Capo Press
1977
Pg. 270:
Music with dinner is an insult both to the cook and violinist.
Gilbert Keith Chesterton (1874-1936)
Quoted in the New York Times, November 16, 1967
 
Google Books
1,911 Best Things Anybody Ever Said
Selected and edited by Robert Byrne
New York, NY: Fawcett Books
1988
Pg. 117:
570
Music with dinner is an insult both to the cook and the violinist.
G. K Chesterton (1874-1936)
 
Google Books
Food and Drink:
A Book of Quotations
Edited by Susan L. Rattiner
Mineola, NY: Dover Publications, Inc.
2002
Pg. 17:
Music with dinner is an insult both to the cook and to the violinist.
G. K. CHESTERTON
 

The Penguin Book of English Song:
Seven Centuries of Poetry from Chaucer to Auden
By Richard Stokes
London: Penguin UK
2016
Pg. 174:
Music with dinner is an insult both to the cook and violinist.
G. K. CHESTERTON: quoted in The New York Times, 16 November 1967