To make sauce: In medium bowl, mix mayonnaise, vinegar, Creole mustard, horseradish, black pepper, garlic and salt until well blended. Cover. Refrigerate at least 2 hours before serving, to blend flavors.
To make chicken: Cover wood chips in water and soak 30 minutes. Season chicken with rub. Drain wood chips. Fill smoker box with wet wood chips. Place smoker box under grill rack on one side of grill before lighting. Close grill.
Prepare grill for indirect medium heat (350-375 degrees). Heat grill by turning all burners to medium. Once cooking temperature is reached, turn off burner(s) on one side. Place chicken on unlit side of grill. Close grill cover.
Grill, turning occasionally, 30-40 minutes, or until internal temperature of thickest part of chicken is 165 degrees. Move chicken to lighted side of grill with skin side down. Turn lighted side of grill to high.
Grill, uncovered, 3-5 minutes longer, or until chicken is charred. Serve chicken with White Barbecue Sauce. Test kitchen tip: Refrigerate any leftover sauce and use as salad dressing, condiment for burgers or dipping sauce for pretzels and vegetables.