Preheat an oven to 375 degrees and prepare a baking sheet with aluminum foil or use a nonstick baking sheet. Throughly rinse produce and pat dry. Zest lime and halve. Cut apple into thick matchsticks. Shuck corn and cut in half. Skewer each half through one end with the bamboo skewers. Rinse chicken breasts and pat dry.
Make the Sauce
In a small mixing bowl, whisk together the mustard, half the brown sugar, half the cider vinegar and the Worcestershire sauce. Season with a pinch of salt and pepper and reserve.
Cook the Chicken
Heat an outdoor grill or grill pan to medium-high heat. Season the chicken with a pinch of salt and pepper and grill. Flip onto second side and brush the sauce onto chicken. Place chicken onto prepared baking sheet and finish cooking in oven another 8-10 minutes, or until internal temperature reaches 165 degrees. Remove from oven and brush one more time with sauce.
Make the Slaw
Place the slaw mix and the apple in a medium mixing bowl. In another small mixing bowl, whisk together the mayonnaise, remaining cider vinegar, remaining brown sugar, juice from half the lime, and a pinch of salt and pepper. Combine with the slaw mix and toss to coat evenly. Season with a pinch of salt and pepper.
Cook the Corn
Drizzle with olive oil, season with a pinch salt and pepper, and place on the grill. Cook, turning often, until the corn is uniformly charred. Remove from the grill and squeeze juice from remaining lime half.
Plate the Dish
Spoon a mound of the apple slaw on the plate and lean a chicken breast against it. Serve the corn alongside and sprinkle the lime zest over the chicken and corn.