In a small bowl, mix together garlic, rosemary, mustard, lemon juice, salt pepper, and olive oil until well blended.
Flatten chicken breasts until they are ~1/2“ thick. Rinse chicken under cold water and pat dry.
Place chicken in a ziploc bag and add most of the marinade, reserving some for basting. Coat the chicken well and marinate for 30 minutes at room temperature, turning the chicken a few times.
Remove chicken from marinade and place on well-oiled grill, turning once and basting with reserved marinade. Cook until internal temperature is 160-165°, remove from grill and let rest, covered with aluminum foil, for 5-10 minutes.