In a medium-sized saucepan over moderate heat, heat oil 1 minute. Add onion and celery and sauté, stirring occasionally, until soft–about 5 minutes. Add garlic and sauté 2 minutes more. Add ketchup, bourbon, stock, molasses, vinegar, mustard, lemon zest and juice, and hot red pepper sauce and bring to a boil over high heat.
Reduce the heat to low and simmer, uncovered, for 20 minutes; set aside or cool, store in a container with a tight-fitting lid and refrigerate for up to 3 days. Gently pull the skin back from the chicken to expose the flesh but do not tear or remove it.
Place in a large self-sealing plastic bag, add half of the sauce, seal and refrigerate for at least 4 hours or overnight, turning occasionally. Refrigerate remaining sauce until ready to use. Preheat the grill.
Remove chicken from bag, reserving sauce. Smooth chicken skin back into place and arrange chicken, skin side down, 12.5 cm (5 inches) above a drip pan over glowing coals. Cover the grill, leaving the vents halfway open (or adjusting for the wind and outdoor temperature).
Cook chicken, turning once, until both sides are browned–15 to 20 minutes. Brush chicken generously with sauce and continue grilling and basting, turning once, until the meat near the thigh bone is no longer pink when cut–25 to 30 minutes more.