Season the chicken on both sides with salt and pepper then set aside. Place a large skillet over medium heat and allow it to get hot. Add oil then place seasoned chicken skin side down into the pan. To make more of the skin come in contact with the heat, place a pot or smaller skillet on top of the chicken to weigh it down.
Allow chicken to fry undisturbed for 8–10 minutes, until skin is crispy and deep golden brown. Flip chicken and cook 3 minutes on the second side then transfer to a plate and set aside. Chicken will still be undercooked at this point.
Remove all but 1 Tbsp of oil from the pan and return pan to heat. Add the sliced onion and cook, stirring frequently for 2–3 minutes until they become translucent. Add garlic and cook for 30 seconds then add the balsamic vinegar, chicken broth, honey and thyme or bay leaf.
Bring liquid to a boil and return chicken and any accumulated juices back into the skillet. Reduce heat to medium-low and allow chicken to cook in simmering sauce 15–20 minutes or until chicken is cooked through and the sauce has reduced and slightly thickened.
Transfer chicken to a serving platter and set aside. Continue simmering the sauce until reduced by half. Remove from heat and stir in butter.
Season with salt and pepper to taste. If necessary, adjust flavor to your liking with an extra splash of balsamic vinegar or a bit more honey. Remove thyme stems or bay leaf and spoon sauce over chicken. Serve immediately.
We chose thighs but you can also use breasts if you prefer!