Preheat. Preheat your grill to 375 degrees F for 2-zone cooking (one direct heat side of the grill with flames and one indirect heat side of the grill without flames). You can also cook this chicken in the oven preheated to the same temperature.
Butterfly the chicken. Use a sharp knife to slice each chicken breast almost all the way in half. Open the slice and press each breast flat.
Make the filling. In a small bowl, combine the cream cheese, cheddar cheese, jalapeno, bacon, and Sweet Rub. Spread 1/4 of the mixture onto each of the butterflied chicken breasts. Fold the breasts over and press the cream cheese mixture so it is evenly distributed within the chicken.
Crush the potato chips. Dump the bag of potato chips into a food processor or blender and pulse until the chips are broken down into crumbs. Alternatively, use a kitchen mallet to crush the chips while they are in a gallon-sized zip-top bag. Pour the crumbs out onto a large plate.
Coat the chicken. Crack the eggs into a pie pan or other shallow dish and beat lightly with a fork. Dip the stuffed chicken breasts into the eggs, then into the chip crumbs, coating each side.
Cook. Once all of the chicken breasts are coated with the eggs and potato chips, place them on your grill or onto a baking sheet and into the oven. Cook for about 25 minutes, or until the internal temperature of the chicken reads 165 degrees F.
Enjoy. Remove the chicken from the grill and serve immediately.