Preheat oven broiler, and set the oven rack about 6 inches from the heat source.
Heat the butter and olive oil in a skillet over medium heat, and pan-fry the chicken breasts for about 10 minutes per side until no longer pink on the inside and golden brown on the outside, sprinkling each side with Creole seasoning.
Scoop the avocados into a bowl, and mash them with the lime juice, tomato, onion, garlic powder, salt, and pepper.
Spoon about 1/3 cup of guacamole onto each chicken breast, top with a slice of pepper jack cheese, and broil for 2 to 4 minutes, until the cheese is melted and bubbling.