Whisk orange juice, lime juice, olive oil, vinegar, garlic, oregano, cumin, paprika, annatto, zest, jalapeño, salt, and pepper.
Stir in the sliced onion. Reserve about 1/4 cup marinade for basting; set aside.
Toss chicken in the remaining marinade to coat well. Chill 30 minutes and up to 8 hours.
Heat a grill to medium-high (about 425°F). Oil the grates lightly.
Shake excess marinade off chicken. Grill skin side down until well marked, 6–8 minutes.
Flip, cover the grill, and cook 12–18 minutes more, basting once with the reserved marinade. Aim for 165°F inside.
If browning too fast, move pieces to a cooler zone. Grill the onions in a basket until tender, if desired.
Rest chicken 5 minutes. Sprinkle with cilantro and serve with the grilled onions.