Heat a grill pan over medium-high heat.
Place peaches halves on grill pan and grill 2 to 3 minutes per side. Set aside to cool and then dice into small pieces.
Season both sides of each chicken breast with 1 teaspoon Jamaican jerk seasoning. Place chicken breasts in pan and grill for 6 minutes per side, or until cooked through.
Meanwhile, in a medium bowl, combine grilled peaches and remaining ingredients. Stir thoroughly.
Serve chicken topped with peach and melon salsa.