Place the chicken in a large mixing bowl. Using a mortar and pestle (or you can use the back of a chef's knife), mash the garlic. In a measuring cup or medium bowl, add the garlic cloves, dried oregano, cumin, salt, pepper and orange and lime juice; stir until combined.
Pour the marinade over the chicken pieces, top with the sliced onions, and refrigerate, covered, for at least 3 hours or overnight.
Remove the chicken and onions from the marinade, drain and pat dry. Reserve the marinade for later use.
Heat the olive oil in a 6-quart cast-iron or heavy-bottomed pot over medium high heat until hot but not smoking. Working in batches, brown the chicken on both sides until the fat is rendered, 2 to 3 minutes per side. Do not overcrowd the pot. Replenish the oil as needed. Set aside the browned chicken pieces.
Pour out all but 2 tablespoons of the oil and saute the reserved onions in the pot until soft and translucent, about 5 minutes. Stir in the reserved marinade and wine and bring to a simmer. Return the browned chicken pieces to the pot and lower the heat.
Cook, partially covered, until the chicken is cooked through, 25 to 30 minutes. Serve with wedges of lime and rice.