Rinse and pat dry chicken pieces. Sprinkle both sides with adobo seasoning.
In a large, heavy bottom, oven proof skillet heat olive oil and butter over medium heat. Once butter has melted add chicken and cook 5-7 minutes on each side or until lightly browned. Transfer to a plate. Set aside.
Reserve 2 tablespoons of pan drippings. Add sliced onions and garlic to the pan. Cook 5 minutes, stirring occasionally. The onion will soften and start to caramelize. Spread onion mixture around in the pan so that it makes a bed for the chicken. Place chicken on top of the onion mixture. Transfer to oven and cook for 20-25 minutes or until chicken is cooked through.
Transfer chicken to a serving platter. Squeeze lime juice over the top and sprinkle with lime zest. Serve.
If you've got an onion-lovin' family be sure to serve the caramelized onions along side.Enjoy!