Prepare the dressing by whisking together the Sunbutter, ginger, honey, fish sauce, chili garlic sauce, lime juice, and 4 tablespoons water. Add more water if needed to thin out the dressing to desired consistency. Set aside.
Place the lettuce is a large salad bowl or on a platter. Arrange the chicken, carrots, cucumber, and radishes in lines atop the lettuce. Garnish with Thai basil leaves and lime wedges. Serve the dressing on the side.