Combine cut-up pieces of chicken with diced peeled apples, any kind of chopped nuts (walnuts, pecans, almonds), raisins and diced celery. Mix with enough mayo to moisten it, a teaspoon of dijon mustard, a little sea salt and either serve it as sandwiches or on lettuce for a nice salad.
Or make a chicken taco soup with canned diced tomatoes, canned corn, black beans or kidney beans or pinto beans (or all 3), taco seasoning, whatever heat your family likes (canned jalapenos, or Rotel tomatoes or mild chilis), sauteed onions and a sauteed red or green pepper, almost anything you can think of that you might like on a taco. Add enough chicken stock or water to make it a soup consistency, heat it well and add the leftover chicken. Serve it with tortilla chips, sour cream and shredded cheese.
Stir fry any vegetables you have (carrots, onions, peppers), add a little soy sauce and some orange juice and let that reduce (a tablespoon of soy, maybe a half cup of orange juice), and stir the chicken in. Serve over rice.
Shred it, mix it with any bottled barbecue sauce, heat through and serve it on buns.
Make a simple white sauce (melt about 4 T butter, add 4 T flour, cook until the flour is absorbed and stir in about 2 cups of milk. Cook over medium heat, stirring, until thickened). Put the leftover chicken, cubed, into a casserole pan, add whatever vegetables you have (thawed, if frozen, and cooked if they're fresh, or drained if they're in a can; carrots, broccoli, peas would all be good), pour the sauce over and sprinkle with shredded cheese. Stir to combine, and bake until heated through.