Brush grill with oil. Prepare grill to medium heat. Puree molasses and next 7 ingredients (red wine vinegar through ground allspice)in blender until smooth.
Season chicken with salt and freshly ground black pepper. Spoon 1/4 cup sauce into a pie plate. Add chicken and turn to coat. Marinate for 15 minutes. Brush plantains with oil and sprinkle with salt and pepper.
Grill plantains and chicken (skin side down), for 8 minutes. Turn chicken and plantains over and grill until chicken is cooked through - approximately 8 minutes (for chicken) and 4 minutes (for plantains).
serve chicken and plantains and drizzle wth remaining sauce.