Preheat oven to 350 F. Trim all visible fat and tendons from chicken breasts. If you did not buy thinly sliced chicken breasts you will need to thin them out first.You can do this by putting the chicken breasts, one at a time, inside a heavy plastic freezer bag and then gently pound with a meat mallet or other heavy object until they are about 1/4 inch thick.
In a medium bowl combine goat cheese and pesto and then stir in the basil.Spread about 2 tbsp of the pesto/basil/goat cheese mixture on each chicken breast. Roll up chicken, starting with smallest end, tucking in loose pieces and securing with two toothpicks.
Put flour, egg whites, and breadcrumbs combined with parmesan cheese into three separate flat dishes. Roll each chicken breast, first in flour, then in egg whites, then in bread crumb/parmesan mixture.
Spray a rimmed baking sheet with nonstick spray and arrange chicken so pieces they are not touching. Bake at 350 F for about 30-40 minutes, or until chicken temperature as reached 165-170.The chicken will be slightly browned and firm to the touch.