Combine marinade ingredients in a shallow dish or large plastic food storage bag. Add chicken and marinate for 1 hour.
Preheat a grill or cast-iron skillet to medium-high heat. Cook chicken 8-10 minutes over direct heat then let rest in pan or over indirect heat for 3-4 minutes more. Place lime halves on the grill or in the pan and slightly char. Thinly slice chicken and douse with juice of charred lime.