Whisk bourbon, sugar, vinegar, Worcestershire, Cajun seasoning, garlic, cornstarch, 1/2 tsp salt, and 1/4 tsp pepper in a bowl until sugar has dissolved.

Pat chicken dry with paper towel and season with salt, pepper, and Cajun seasoning. Heat oil in large non-stick skillet over medium-high heat until just smoking. Cook chicken, skin-side down, until skin is well browned and crisp, 15-20 minutes. Carefully turn chicken skin-side up and cook over medium heat until meat registers 175F, 5-8 minutes. Transfer chicken to platter.

Pour off excess fat from skillet and add bourbon mixture, simmering until thickened, about 2 minutes.