Place the chicken breasts between two piece of plastic wrap or wax paper and pound to an even thickness with a meat mallet or rolling pin.
Mix the olive oil, lime zest, lime juice, cilantro, sugar, salt and pepper together in a large bowl. Add the chicken and massage the marinade into the chicken. Cover and chill for at least 30 minutes, and up to 4 hours or overnight.
Preheat the grill for medium high heat. Remove the chicken breasts from the refrigerator. Remove them from the marinade and pat them dry with paper towels. Coat the chicken breasts with some olive oil. Soak a paper towel in a little more oil and use tongs to wipe the grill grates. When the grill is hot, place the chicken breasts on the grill. Grill for a few minutes on each side, until cooked through.