For the sauce: Stir together the chicken broth, balsamic, maple syrup, salt and pepper. Set aside.
In a 10 to 12-inch skillet (large enough to hold all your chicken with a bit of space in between), heat oil over medium-high heat until shimmering. Add chicken, skin-side down and cook until the skin is deep golden, about 5 minutes. Flip chicken over and cook the other side for 3-4 minutes. Remove chicken to a plate and discard all but about a teaspoon or two of the fat in the pan.
Return the pan to the burner and stir in the garlic slices. Cook, stirring, until just softened and fragrant, 30-40 seconds. Pour in the sauce and bring to a boil. Reduce heat to medium-low. Return chicken to the pan, skin side up and allow to simmer 10-15 minutes, spooning some of the sauce overtop of the chicken a time or two, until chicken is cooked through. If sauce is not thick enough, you can stir in a mixture of 2 tsp cornstarch with 2 Tbsp water and cook, stirring, until sauce thickens.
Be sure to check out the Cook's Notes in the post for more tips and tricks for making this recipe!