I don't know if this is the recipe in question, but it's one in my collection of Blue Books.
This is from the Ball Blue Book
Volume 1, Published by Alltrista Corp. copyright 1995, 1997, 1998, Page 59
Chicken a la King
True chicken a la King is made of all white meat, pure cream and sherry wine.
The recipe given here is for a product suitable for canning or freezing.
2 (3 1/2 to 4 pounds) stewing chickens, cut into pieces
2 stalks celery, quartered
1 onion, quartered
1 carrot, quartered
4 peppercorns
2 whole allspice
1 bay leaf
2 teaspoons salt
1/4 cup chicken fat or butter
1/2 cup flour
5 cups chicken broth
1/2 cup chopped celery (about 1 stalk)
1/4 cup chopped pimento
1 tablespoon chopped parsley
Salt and pepper to taste
Combine chicken, celery stalks, onion, carrot, peppercorns, allspice, bay leaf, and salt in a large sauce pot.
Cover with water. Bring to a boil; reduce heat; simmer 2 to 3 hours or until chicken is tender.
Remove and discard vegetables. Allow chicken to cool in broth. Remove chicken. Skim off excess fat; strain broth.
Remove skin and bones from meat. Cut meat into 1-inch pieces.
Melt fat or butter; add flour, stirring until smooth. Gradually add chicken broth and cook until thickened, stirring constantly.
Add chicken and remaining ingredients. Simmer 5 minutes. Pack hot meat and sauce into hot jars, leaving 1-inch head space.
Remove air bubbles. Adjust two-piece caps.
Process pints 1 hour and 5 minutes, quarts 1 hour and 15 minutes, at 10 pounds pressure in steam-pressure canner.
Yield: about 4 pints or 2 quarts.
To serve: Brown mushrooms in butter, add mushrooms to Chicken a la King, if desired. Heat until hot throughout.