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.
I used a grill pan to prepare these they were pretty good, but I'm sure they would've been much better on an real charcoal grill; will do that way next time. Served with grilled zucchini, which is always good, in a grill pan or on a charcoal grill.
Changes I made: I used agave syrup instead of sugar and did not add that much pepper. The taste is addictive. Don't overcook, but let them rest to finish cooking and they are juicy and taste very good without any sauces. Served with rice and frozen mixed vegetables (well, it WAS a weeknight).
Made this last night for dinner after searching for something to do with thawed chicken breasts. Threw all the ingredients together, not really measuring, as I wasn't in the mood for the 'formality'. These came out fantastic! The lime and the sugar make an awesome flavor combo. My husband couldn't stop raving and asked for them again tonight for dinner!
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