Make the marinade. In a small bowl mix the soy sauce, peanut butter, sugar, vinegar, garlic, oil, hot sauce and pepper. Stir with a fork until the peanut butter is incorporated. Reserve 1 tablespoon of the sauce for serving.
Marinate the chicken. Add the chicken and the remaining sauce to a zip-top plastic bag and marinate in the refrigerator for at least 15 minutes (since this is not an acidic marinade you can leave it longer if you want).
Preheat the grill. While the chicken is marinating preheat a grill to medium-high heat (about 450°F).
Grill the chicken. Grill the chicken for 6 minutes per side or until an internal temperature of 165°F is reached. Remove the chicken from the grill.
Make the coleslaw. While the chicken is grilling mix the mayonnaise, sour cream, vinegar, lime juice, oil and ginger in a small mixing bowl. Add the coleslaw mixture and toss to coat.
Serve. To serve, divide the coleslaw mixture between two plates. Top each salad serving with a chicken breast. Drizzle some of the reserved sauce over the top and serve immediately.