Heat broiler, with rack set 4 inches from heat. Line a rimmed baking sheet with aluminum foil. In a shallow dish or resealable plastic bag, combine vinegar, mustard, garlic, 1 teaspoon salt, and 1/4 teaspoon pepper; add chicken, and turn to coat. Marinate at room temperature for 10 minutes (or cover and refrigerate in marinade up to 24 hours).
Lift chicken from marinade, and place on prepared baking sheet; broil (without turning) until opaque throughout. Transfer chicken to a work surface; discard pan juices from baking sheet.
Place baguette pieces on baking sheet, cut side up; dividing evenly, spread with apricot preserves, and layer with chicken, ham, and then cheese. Broil until cheese is melted, 4 to 6 minutes.