Place chicken on a cutting board, cover with a sheet of plastic wrap and pound thicker parts of chicken to an even thickness. Transfer chicken to a resealable plastic bag.
In a small mixing bowl whisk together lime zest,lime juice, olive oil, honey, garlic and season with 1 tsp.
Salt and 1/2 tsp pepper. Pour marinade mixture over chicken in the bag. Seal the bag, then rub marinade over chicken. Allow to rest in refrigerator 2 - 4 hours.
Preheat a grill over medium-high heat. Brush the grill grates lightly with oil then grill the chicken for
about 4-5 minutes per side, or until it's fully cooked through. Remove and let it rest for 5 minutes covered with foil.
Meanwhile, in a medium mixing bowl toss together avocado, mango, tomato, onion, garlic and lime and season with salt and pepper to taste.
Spoon a generous amount over chicken and sprinkle with fresh chopped parsley, cilantro, or mint.