Make the dressing: Whisk the cherries, 1 tablespoon reserved cherry juice, the soy sauce, peanut butter, vinegar, vegetable oil and sesame oil in a bowl. Set aside.
Make the chicken: Put the cherries, 3 tablespoons reserved cherry juice, the soy sauce, white wine, brown sugar, Worcestershire sauce, ginger and garlic in a blender and puree until the cherries and garlic are finely chopped. Pour the marinade into a large resealable plastic bag. Pierce the chicken all over with a fork. Add to the bag with the marinade, seal and refrigerate at least 20 minutes or up to 8 hours. Preheat a grill to high. Brush the grates with vegetable oil. Remove the chicken from the marinade, brushing off any excess. Grill the chicken, covered, until the juices run clear, 5 to 7 minutes per side. Transfer to a cutting board and let rest 5 minutes.
Meanwhile, prepare the salad: Preheat the oven to 350 degrees F. Soak the sauerkraut in a bowl of ice water 10 minutes; drain, rinse and squeeze out the excess water. Arrange the wonton strips in a single layer on a baking sheet and bake until crisp, about 5 minutes. Toss the sauerkraut and romaine with half of the dressing in a bowl; divide among plates. Top with the bell peppers, scallions, carrots, snow peas and water chestnuts. Slice the chicken and serve with the salad. Top with the crispy wonton strips. Serve with more dressing on the side. Photograph by Yunhee Kim