Season both sides of the chicken breast liberally with Italian seasoning, salt, and black pepper on a cutting board.
Place the chicken breast on a grill or in a grill pan with a sprinkle of olive oil over medium-high heat and cook for 5-6 minutes each side, flipping just once, until cooked through or an internal temperature of 165 oF is attained. Remove off the grill and lay aside for 1-2 minutes to rest before slicing into thin strips.
Meanwhile, slice the mozzarella and tomato into 1/4-1/2-inch thick slices and leave them.
When the chicken is done and resting, split the ciabatta in half, decrease the heat to medium, and set the bread, cut side down, on the grill or pan for 1-2 minutes until golden. Remove from the pan and set aside after done. (Alternatively, preheat the oven to broil and toast the ciabatta, cut side up, for 1-2 minutes.)
Assemble your sandwich by spreading pesto on the bottom half of each toasted ciabatta, then layering with sliced chicken, sliced mozzarella, tomato slices, a sprinkling of salt & pepper, fresh basil leaves, and a drizzle of balsamic glaze, if preferred.