Place chicken in a 9 x 13-inch non-reactive baking dish.
In a blender combine salt and pepper, Seville orange juice (or orange and lime juices), garlic, oregano, and cumin. Blend on high until smooth.
Pour marinade over chicken and top with onion slices. Cover and refrigerate at least 2 hours or up to overnight.
Heat a charcoal or gas grill to medium-low heat. Remove chicken from marinade, letting excess drip back into the dish. Grill, turning occasionally, until chicken is cooked through, about 30-40 minutes. During the last 15-20 minutes of cooking time, add onion slices to the grill and grill onions until tender and lightly charred.