Slice the chicken breasts in half sideways to make two thinner pieces from each one, for a total of four pieces. Cut open the avocado, remove the meat to a bowl, and mash it until creamy. Slice the tomato in ¼ inch thick slices.
Melt the butter with the garlic in a large skillet. When the pan is hot and butter is bubbling, add the chicken. Cover and cook on medium-high about 4 minutes per side. When the chicken is about 2 minutes from being done, remove the cover and spread avocado on top of each piece. Add tomato slices on top of the avocado, then top with cheese. Cover again and cook for one additional minute. Remove from heat, but leave the cover on until the cheese is melted. Serve with vegetable and a starch if desired.