Pat chicken dry, season with salt and pepper, and let sit 10–30 minutes
Heat a large skillet over medium with oil, add chicken skin-side down, and cook undisturbed until skin is deeply golden and crisp, 20–25 minutes (adjust heat as needed)
Add garlic, flip chicken, and cook until cooked through, about 5 minutes, then transfer chicken to a plate and remove all but 3 Tbsp fat
Add stock, lime juice, and maple syrup to the pan, season, bring to a simmer, and reduce by half, about 3 minutes
Whisk in butter until the sauce is glossy and thick, then serve chicken with sauce, lime wedges, and herbs
