1. Combine mayonnaise, cilantro, 3 Tbsp. vinegar, 1/4 tsp. salt, and 1/8 tsp. pepper in a small bowl. Reserve 3/4 cup mayonnaise mixture. Brush chicken with remaining 1/4 cup mayonnaise mixture.
2. Preheat grill to 350° to 400° (medium-high) heat. Grill chicken and corn at the same time, covered with grill lid. Grill chicken 7 to 10 minutes on each side or until done; grill corn 14 to 20 minutes or until done, turning every 4 to 5 minutes and basting with melted butter.
3. Toss coleslaw mix with oil, sugar, 1/4 tsp. pepper, and remaining 3 Tbsp. vinegar and 1/2 tsp. salt. Season chicken and corn with salt and pepper to taste. Serve with coleslaw and reserved mayonnaise mixture.