Prick the chicken pieces all over with a fork and place them aside.
In a large bowl, whisk together the balsamic vinegar, half of the lemon zest, salt, and black pepper.
Add the chicken and coat well with the marinade. Refrigerate for at least 20 minutes.
In a small bowl, combine the sugar with the remaining lemon zest.
Preheat the oven to 400°F.
Heat the oil in a large oven-safe skillet over medium-high heat until very hot.
Melt 2 tablespoons of butter in the skillet.
Place the chicken skin-side down in the skillet along with any remaining marinade.
Cook for 3 to 4 minutes until deeply browned, then flip and cook for 1 additional minute.
Sprinkle the lemon sugar evenly over the chicken.
Transfer the skillet to the oven and roast the Balsamic Lemon Chicken for about 25 minutes or until the internal temperature reaches 165°F.
Remove the skillet carefully from the oven.
Scatter the remaining butter pieces around the chicken and pour fresh lemon juice over everything.
Allow the butter to melt into the pan sauce before serving.
Serve warm with lemon wedges and spoon the flavorful sauce over the chicken.