Preheat grill for medium heat and lightly oil the grate. Season chicken breast halves with salt and black pepper.
Stir peach preserves, olive oil, soy sauce, garlic, and mustard in a bowl; season with salt and black pepper. Reserve about 1/2 cup peach sauce.
Place chicken on preheated grill; cook until golden brown, 6 to 7 minutes, then flip chicken. Continue cooking for 5 to 6 minutes. Brush both sides of the chicken with peach sauce. Cook until no longer pink in the center and the juices run clear, 4 to 5 more minutes. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C).
Arrange peach halves cut side down on the grill. Grill for 2 minutes, flip, and brush with reserved 1/2 cup peach sauce. Continue to grill until peaches are tender, 3 to 4 minutes more.
