My recipe isn't as classy as Andy's, but it makes a delicious country gravy. Remove chicken from pan. Whisk flour into the chicken fat to make a roux, (cook a few minutes if you want), whisk in chicken broth & milk, stir and cook on medium to med/high heat until thickened, then season with S&P and a pinch of sugar. A pinch of thyme and/or sage would be a good addition.
Here's my rule...1 tsp fat, 1 tsp flour, 1 cup liquid. I usually just eyeball it. I go half/half on the broth and milk.
If you don't want a white gravy, use all broth or half broth and half water.