In a large mixing bowl, prepare the marinade by adding olive oil, lime juice, zest, oregano, garlic, and salt & pepper.
Add chicken breasts to a gallon-size sealable storage bag and pour marinade mixture over top. Seal bag and turn to coat breasts thoroughly. Place the bag in the refrigerator to marinate for at least 1 hour to overnight. Turn the bag a couple times to evenly distribute the marinade during this time.
Remove chicken from the refrigerator and discard excess marinade. Grill the breasts over medium direct heat, turning once, for 10-12 minutes total. Remove from heat and rest for 5 minutes before serving.