In a large zip-top plastic bag, combine chicken breasts, salsa verde, olive oil, lime juice, cumin, salt, and pepper. Seal the bag and massage the marinade into the chicken to coat evenly. Refrigerate to marinate for at least 30 minutes, or overnight for deeper flavor.
Preheat the grill to medium-high heat and lightly oil the grill grates.
Grill the chicken for about 5 minutes on the first side with the grill lid closed. Flip and cook for an additional 4 minutes on the second side, or until the chicken is fully cooked.
Reduce the grill temperature to medium-low. Place a slice of pepper Jack cheese on each chicken breast, close the grill lid, and cook for about 1 minute, or until the cheese has melted.
Serve the chicken garnished with optional cilantro and lime wedges. Adjust seasoning with additional salt, pepper, or salsa as desired.