Preheat oven to 375 degrees. Slice each chicken breast crosswise so you have 2 thinner breasts. You should end up with 4 thin breasts. Place chicken in a glass baking dish. Season with salt and pepper. Drizzle with olive oil. Roast for 20-25 minutes.
Dice the chipotle peppers. In a small bowl, combine the mayonnaise, lime juice and peppers. Season with salt and pepper. Set aside.
Heat a griddle or skillet over medium heat. Slice the bread into 8 thick slices (about 1/2 inch) and spread one side with softened butter or mayonnaise.
Build the sandwich: Spread chipotle mayonnaise onto the unbuttered side of the bread. Layer the grated cheddar, sliced avocados, cooked chicken and 2 slices of American cheese and top with another slice of bread. Grill until golden and melted, 3-4 minutes each side.