Combine lime juice, sugar, pepper, oil, salt, and 1/4 cup water in a large bowl or resealable plastic bag. Stir to dissolve sugar and salt. Set aside.
On a flat surface, lay 1 chicken breast half between 2 large pieces of plastic wrap. Using a mallet or a small saucepan, pound chicken to an even 1/4- to 1/3-in. thickness. Put chicken in bowl or plastic bag with marinade. Repeat with remaining breasts. Cover or seal; chill 30 minutes.
Preheat a gas or charcoal grill to medium-hot (you can hold your hand 1 to 2 in. above cooking-grate level only 3 to 4 seconds). Remove chicken from marinade and grill 4 minutes (cover if using gas). Turn chicken over (cover if using gas), and grill until cooked through (chicken should feel firm when poked), 3 to 4 minutes. Serve hot or at room temperature.
Note: Nutritional analysis is per serving.