Whisk together lime juice, soy sauce, and oil in a bowl. Place chicken breasts on a work surface between two layers of waxed paper or plastic wrap. Using the smooth side of a meat pounder, pound the chicken breasts until all the pieces are an even A-inch thickness.
Place chicken breasts in a resealable plastic bag or glass baking dish. Pour marinade into bag or over chicken in dish. Refrigerate at least 3 hours or overnight.
Heat a grill or grill pan over medium heat. Remove chicken from marinade, letting excess drip off. Grill chicken until cooked through, about 3 minutes per side. Shred or slice chicken, and serve with lettuce leaves and herbs on the side. See the top left tin for reference.
I tried this with both chicken and beef. It was wonderful! Excellent marinade! The fresh mint and cilantro were great in the salad as well, which we ate with this site's Cilantro-Lime Dressing (do a search). Simply fantastic!