Preheat an outdoor grill for medium-high heat and lightly oil the grate.
Whisk garlic, olive oil, rosemary, mustard, lemon juice, ground black pepper, and salt together in a bowl.
Place chicken breasts in a resealable plastic bag. Pour garlic mixture over chicken, reserving 1/8 cup. Seal bag and massage marinade into chicken. Let stand for 30 minutes at room temperature.
Place chicken on preheated grill and cook for 4 minutes. Turn the chicken, baste with reserved marinade, and continue to grill until cooked through, about 5 minutes. Cover with foil and let rest for at least 2 minutes before serving.