Stir together lemon juice, garlic, oil, rosemary, salt, pepper, and mustard in a bowl until well combined. Using a fork, prick each chicken breast all over 8 to 10 times.
Add chicken breasts to bowl with lemon juice mixture and toss to coat completely, using your hands to gently massage lemon juice mixture into each chicken breast. Cover bowl with plastic wrap and refrigerate for 1 hour.
Preheat an outdoor grill for medium-high heat and lightly oil the grate.
Place chicken breasts on oiled grates; grill, covered, until chicken breasts are lightly charred, no longer pink in the center and the juices run clear, 10 to 12 minutes per side. An instant-read thermometer inserted into the center should read 165 degrees F (74 degrees C).
Transfer chicken breasts to serving platter; serve with lemon wedges.