Make marinade: In a blender, combine scallions, garlic, jalapeno, lime juice, oil, sugar, allspice, thyme, cinnamon, 1 teaspoon salt, and 2 tablespoons water; blend until smooth. Set aside 1/4 cup for brushing.
Place chicken in a shallow dish; season all over with salt. Pour remaining marinade over chicken; toss to coat. Cover; refrigerate, turning once or twice, at least 2 hours, or up to overnight.
Heat grill to medium-high; oil grates. Lift chicken from marinade, letting excess drip off (discard marinade); place on grill, and cover. Cook, turning occasionally, until chicken is blackened in spots, about 10 minutes.
Move chicken to a cooler part of the grill; brush with reserved marinade. Grill, covered, until chicken is cooked through, 10 to 15 minutes more. Serve immediately.
If you add in some Scotch Bonnet peppers, you'll get the right heat factor. Just BE CAREFUL! The first time I used Scotch Bonnets I made the mistake of rubbing my nose and mouth. Even after scrubbing my hands with soap and water for minutes, the oils were still there. I ended up dunking my face in milk and wearing gloves the rest of the night (to be safe!...needless to say, I looked ridiculous!! Good thing I was cooking alone.). Lesson: WEAR GLOVES when working with Scotch Bonnets. ;)
This was pretty tasty, but not very hot, as jerk should be. I even doubled the peppers and didn't seed them. I used boneless chicken breasts instead of bone-in pieces and cooked them accordingly.