Preheat a grill pan or panini press over medium heat.
Season the chicken breasts with Italian seasoning, salt, and pepper. Drizzle with olive oil.
Cook the chicken on the grill pan for about 6-7 minutes per side, or until fully cooked and the internal temperature reaches 165°F. Remove from heat and let rest for a few minutes before slicing.
Assemble the panini by layering sliced chicken, mozzarella, tomato, and basil on one slice of bread. Drizzle with balsamic glaze and top with another slice of bread.
Place the assembled sandwich on the grill pan or in the panini press. Cook for about 3-4 minutes, or until the bread is golden brown and the cheese is melted.
Remove from heat, slice in half, and serve immediately.