Use a paper towel to pat the chicken dry. Generously season on all sides with salt and pepper. In a large dish, whisk together the jam, dressing, vinegar and garlic and toss with the chicken. Cover and refrigerate for 4 to 6 hours.
Preheat the oven to 350 degrees F.
Remove the chicken from the marinade and place on a baking sheet; reserve the extra marinade. Bake for 45 minutes, then remove the baking sheet from the oven and increase the temperature to 425 degrees F. Spoon the resesrved marinade over the chicken and sprinkle with the brown sugar. Bake until the glaze on the skin is caramelized, about 15 minutes more.
Serve the chicken on a platter and pour any additional marinade from the baking sheet over it.