Whisk lime juice, cilantro, garlic salt, and black pepper together in a large glass or ceramic bowl. Add chicken; toss to evenly coat. Cover the bowl with plastic wrap and marinate in the refrigerator, 30 minutes to overnight.
Preheat an outdoor grill for medium-high heat and lightly oil the grate.
Remove chicken from marinade and shake off excess. Discard remaining marinade.
Cook chicken on the preheated grill, turning occasionally, until no longer pink at the bone and juices run clear, about 30 minutes. An instant-read thermometer inserted near the bone should read 165 degrees F (74 degrees C).