Season chicken breasts with salt and pepper. Heat olive oil in a skillet over medium heat and cook chicken until golden and cooked through.
In a small bowl, mix mayonnaise and Dijon mustard. Set aside.
Slice avocado, red onion, and tomato while the chicken rests.
Lightly butter one side of each bread slice.
On the unbuttered side, spread the mayo-mustard mix. Layer chicken, avocado slices, cheese, tomato, and red onion.
Close sandwiches and grill in the skillet, buttered side down, until bread is golden and cheese is melted.
Flip carefully and cook the other side until crispy and golden.
Slice in half and serve warm.