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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).
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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.
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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.