Open chicken thighs and lay flat. Divide chilies in four equal amounts and place in the center of each thigh. Roll up and secure with toothpicks.

In a shallow bowl, combine eggs and salt and pepper to taste. Dip thighs in egg and roll in bread crumbs. Refrigerate 15 minutes.

In a large skillet, over medium heat, melt butter with oil. Add thighs and cook, turning, 10-12 minutes or until brown on all sides.

Spoon tomato sauce over thighs. Reduce heat to medium-low and cover. Cook for 20 minutes or until thighs are cooked through.

Sprinkle with cheese; cover and cook 2 minutes longer.