To prepare citrus mayonnaise, combine first 5 ingredients in a small bowl.
To prepare the sandwiches, sprinkle chicken with salt and pepper. Place a large nonstick skillet coated with cooking spray over medium-high heat; add chicken. Cook 5 minutes on each side. Reduce heat to low. Cover; cook 5 minutes or until done. Remove from heat. Cut chicken diagonally across grain into thin slices.
Spread 1 tablespoon citrus mayonnaise on each of 4 bread slices. Top with 1 lettuce leaf, 1 chicken breast half, 2 tomato slices, 2 avocado wedges, and remaining bread slices.