Whisk together 3 tablespoons cider vinegar, molasses, olive oil, allspice, salt and pepper.
Arrange chicken in 11x7-inch dish pour marinade over, turning chicken to coat. Cover; refrigerate for 30 minutes.
Remove chicken from marinade, discard marinade. Grill 3 to 4 minutes on each side or until no longer pink in center. Keep covered and warm.
Combine remaining vinegar and honey in bowl; stir. Cook bacon over moderate heat, large skillet, stirring, until crisp. Crumble bacon. Reserve 2 tablespoons bacon fat.
Heat bacon fat over medium-high heat until hot but not smoking ; cook caraway seeds, stirring until fragrant, about 30 seconds. Add coleslaw mix, vinegar mixture and salt and pepper to taste and cook, stirring, until cabbage is just wilted about 1 minute.
Remove skillet from heat; add green onions and bacon. Toss together. Plate slaw on 6 different dishes and place cooked chicken on top of slaw to serve.