Preheat the grill or grill pan to medium-high heat.
Place the chicken between two sheets of parchment paper and pound with a meat mallet or rolling pin until about 3/4-inch thick.
Rub the chicken on both sides with 1/2 tablespoon olive oil and season with sea salt and freshly ground black pepper.
Grill the chicken 5 to 6 minutes per side, until an instant-read thermometer inserted into the thickest part reads 165°F (74°C).
During the last 2 minutes of cooking, place the ciabatta rolls cut-side down on the grill and toast until lightly browned.
Spread 1 tablespoon pesto on each half of the toasted rolls.
Divide the mozzarella between the bottom halves of the rolls, top with the hot grilled chicken, then add sliced tomato, arugula, and fresh basil leaves.
Cover with the top halves of the rolls and serve immediately.