In a large bowl, combine olive oil, fresh orange juice, fresh lime juice, minced garlic, dried oregano, ground cumin, salt, and black pepper. This mix of citrus juices creates the base of your mojo marinade.

Place the chicken breasts in a large resealable plastic bag. Pour the marinade over the chicken, ensuring all pieces are well coated. Seal the bag and refrigerate for at least 2 hours, preferably overnight, to allow the flavors to meld.

Preheat your grill to mediumhigh heat. For best results, ensure the grill grates are clean and lightly oiled to prevent sticking.

Remove the chicken from the marinade and discard the marinade. Grill the chicken breasts for 67 minutes per side, or until the internal temperature reaches 165 degrees F. Use a meat thermometer to check for doneness.

Serve your Cuban Grilled Mojo Chicken with a side of black beans, rice bowls, or fresh green beans for a complete meal. Garnish with fresh cilantro and a squeeze of lime zest for extra flavor.