Puree in blender lime juice, soy sauce, oil, hot-pepper sauce, ginger, garlic, thyme, pepper, allspice and salt. Combine marinade with chicken in plastic food-storage bag. Seal. Marinate in refrigerator overnight.
Place oven rack in top position. Heat oven to 500°F.
Drain chicken; discard marinade. Pat dry. Arrange in roasting pan.
Roast on top rack in 500°F oven 25 minutes for breasts, 30 minutes for thighs and drumsticks, or until instant-read thermometer registers 170°F, without touching bone.