Combine the chicken, ham, and egg in a large bowl until well blended. Gradually add bread crumbs until the mixture loses its stickiness and can be easily formed into balls.
Form the chicken mixture around the cheese cubes, forming 2 inch balls. Place on a plate.
Heat 1 1/2 inches of oil in a deep skillet to 350 degrees F (175 degrees C). Fry the balls until the outsides are golden brown, about 4 minutes. Drain on paper towels, and place in baking dish.
Bake in preheated oven until cooked through and cheese is soft, about 20 minutes. Cool briefly before serving.
