Combine all marinade ingredients (cilantro, garlic, olive oil, lime juice, lime zest, and all seasonings) in a food processor. Blend until ingredients are well combined.
Pour ingredients into a large ziploc bag. (Reserve a couple tablespoons for basting.)
Add chicken breasts to bag. Marinate chicken for 2 hours up to overnight.
When ready to cook, heat grill to medium heat. Remove chicken from ziploc bag with tongs and place onto hot grill.
Cook chicken slowly so it stays juicy. Let grill for 10-15 minutes per side, until cooked through.
Once chicken is cooked through, remove from grill and set aside. Brush with extra marinade and let rest for 5 minutes.
Slice into strips before serving.