Place chicken breast halves in a gallon-size resealable plastic bag and add marinade. Refrigerate for 1 hour.
Preheat oven to 450 degrees F (230 degrees C). Line a sheet pan with heavy-duty aluminum foil.
Place butternut squash, brussels sprouts, baby carrots, and apple on the sheet pan. Drizzle with olive oil and sprinkle with salt and pepper. Place marinated chicken breasts on top of vegetable-fruit mixture and drizzle with leftover marinade from bag.
Bake in the preheated oven until chicken is no longer pink and the juices run clear, 25 to 30 minutes. An instant-read thermometer inserted into the center should read 165 degrees F (74 degrees C). Turn on the oven's broiler. Broil until vegetables are lightly browned, 2 to 3 minutes.