1. In a large bowl, whisk together the ketchup, molasses, mustard, vinegar, Worcestershire sauce and soy sauce. Reserve 1/2 cup of the sauce for serving; add the chicken breasts to the remaining sauce in the bowl and turn to coat. Set aside.
2. Make the slaw: In a large bowl, stir together the mayonnaise, vinegar and sugar. Add the onion and chives, then add the cabbage and toss well. Season generously with salt and pepper and toss.
3. Light a grill or preheat the broiler. Grill or broil the chicken for about 10 minutes, turning once, until nicely charred and cooked through.
4. Slice the chicken crosswise on the diagonal. Spoon some of the reserved barbecue sauce on the bottoms of the buns and arrange the chicken on top. Spoon the remaining sauce over the chicken and mound the napa slaw on top.