Preheat oven to 350F.
Butterfly the chicken breasts (if you aren't sure how to http://www.foodnetwork.com/food/ck_dm_meat_poultry/article/0,1904,FOOD_19002_2370613,00.html )
Mix the chili powder, cayenne, Salt and pepper and bread crumbs together. Beat the eggs in a seperate dish.
Open the breasts up, smear the chilis on the inside and layer slices of cheese on one inside. Then close the chicken breast so you have the chilis and cheese inside. Dip in egg and then dredge in bread crumbs. Place the chicken on a baking dish preferably with a rack.
Bake at 350F for approximately 30 mins - 45 mins.