Spread mayonnaise on one side of each bread slice.
Layer chicken, tomato slices, avocado, and shredded cheese on one slice of bread.
Top with the second slice, mayo side down.
Butter the outer sides of the sandwich.
Heat a skillet over medium heat and grill the sandwich for 3–4 minutes per side until golden and the cheese is melted.
Remove from heat, slice, and serve hot.