Make a marinade with the orange juice, lime juice, olive oil, garlic, smoked paprika, achiote paste, cumin, oregano, white vinegar, salt, and pepper.
Cut the chicken in half by removing the backbone and cutting down the middle.
Place the chicken pieces in a ziplock bag and pour in the marinade. Refrigerate for 1-4 hours, turning occasionally.
Grill the chicken over medium-low heat, flipping and basting with the reserved marinade until cooked through, about 10-15 minutes per side.
Serve the grilled chicken.