Combine oil, lime juice, green onion, habanero chiles, garlic, thyme, ginger, brown sugar, allspice, salt, and pepper in a food processor or blender and pulse until well blended. Reserve 1/4 cup of the mixture in a small bowl. Cover and refrigerate until ready to use. Transfer remaining mixture into a large resealable bag. Add chicken, seal bag, and chill for 3-8 hours.
Grease and preheat grill OR preheat oven to 425 degrees. Remove chicken from bag, discard the bag and remaining marinade. Grill chicken 5-6 minutes on each side OR if using oven method, bake on a greased sheet pan for 15 minutes, then broil for 3-5 minutes.
Brush reserved sauce over the chicken and cook 2-3 minutes longer on each side until cooked through. Garnish with chopped cilantro if desired and serve immediately.