Whisk vinegar, oil and salt in a medium bowl. Stir in shallots and garlic. Add chicken and toss to coat. Cover and marinate in the refrigerator for 20 minutes to 3 hours.

Meanwhile, soak wood chips in a bowl of water for 20 minutes.

Fold a 12-by-20-inch piece of heavy-duty foil in half to create a 12-by-10-inch double-thick piece. Transfer wet wood chips to the center of the foil, allowing as much water as possible to drip back into the bowl. Create a packet by folding the short ends of the foil over the wood chips and folding the open ends to seal them.

Place the packet of wood chips, pierced-side up, under the grill rack and on top of the burners. Close the lid. Turn the heat to high and allow the grill and packet to heat until the chips smell smoky and smoke begins to billow from under the lid, about 15 minutes (don't worry if the packet temporarily catches on fire). Make 6 holes in the top of the foil packet using a skewer or the tip of a knife.

Transfer the chicken to the grill, allowing excess marinade to drip back into the bowl (discard marinade). Grill the chicken, turning once, until cooked through, 6 to 8 minutes per side. Serve hot or chilled.

MAKE AHEAD TIP: Marinate the chicken for up to 3 hours.