Prepare the marinade and chicken:

• Whisk ½ cup of beer, garlic, lime juice, soy sauce, salt, mustard, pepper, thyme, and cumin together in liquid measuring cup.
• Refrigerate remaining beer, still in can, until ready to grill.
• Using your fingers or the handle of a wooden spoon, gently loosen the skin covering the chicken breast and leg quarters. If using thighs or leg quarters, loosen the skin covering the meat accordingly.
• Using a paring knife, poke 10 to 15 holes in the fat deposits on the skin of the back.
• Tuck the wingtips underneath chicken.

Marinate the chicken:

WHOLE CHICKEN:

• Place the chicken in a bowl with the cavity end facing up.
• Slowly pour the marinade between the skin and meat and rub the marinade inside the cavity, outside the skin, and under the skin to distribute.
• Cover and refrigerate for 24 hours, turning the chicken halfway through marinating.

THIGHS ONLY:

• Place the thighs or leg quarters in a 2-quart zipper bag set in a large bowl.
• Pour in the marinade.
• Seal the bag, pushing out excess air.
• Try to work the marinade into the chicken and under the skin by scrunching the meat from the outside of the bag.
• Place in the refrigerator for at least 2 hours and up to 24 hours, turning the bag over at least once halfway through the marination time.

FOR THE OVEN:

• Heat the oven to 450 degrees. Use the convection setting if available.
• Remove the chicken from the marinade and pat dry with paper towels.
• Arrange skin-side up on a cooling rack set in a rimmed baking sheet and drizzle the chicken with oil.
• Place the baking sheet in the oven and roast until the skin is golden and the chicken is cooked through, 30 to 40 minutes (35 to 45 minutes if using leg quarters), turning the sheet pan half way around after 15 minutes.
• Remove from the oven and let sit, loosely covered with foil, for 10 minutes before serving.
• Note: The remaining recipe applies only to grilling a whole chicken.

Prepare the wood packet:

• Using a large piece of heavy-duty aluminum foil, wrap the wood chips in a 8 by 4½-inch foil packet. (Make sure the chips do not poke holes in the packet.)
• Cut 2 evenly spaced 2-inch slits in the top of the packet.

Prepare the chicken for the grill:

• Place the beer can in a large, shallow bowl.
• Spray the can all over with vegetable oil spray.
• Slide the chicken over the can so the drumsticks reach down to bottom of the can and the chicken stands upright; set aside at room temperature while preparing the grill.

FOR A CHARCOAL GRILL:

• Open the bottom vent fully and place a disposable pan in the center of the grill.
• Light a large chimney starter two-thirds filled with charcoal briquettes (4 quarts).
• When the top coals are partially covered with ash, pour into 2 even piles on either side of a disposable pan.
• Place the wood chip packet on 1 pile of coals.
• Set the cooking grate in place, cover, and open the lid vent fully.
• Heat the grill until hot and the wood chips are smoking, about 5 minutes.

FOR A GAS GRILL:

• Remove the cooking grate and place the wood chip packet directly on one of the outside burners.
• Set the grate in place; turn all burners to high; cover; and heat the grill until hot and the wood chips are smoking, about 15 minutes.
• Turn the 2 outside burners to medium and turn off the center burner. (Adjust outside burners as needed to maintain grill temperature between 350 and 375 degrees.)

Grill the chicken:

• Scrape the cooking grate clean with a grill brush.
• Transfer the chicken with the can to the center of the cooking grate with the wings facing the piles of coals (or the outer burners on the gas grill) at 3 and 9 o’clock (the ends of the drumsticks should rest on the grate to help steady the bird).
• Cover the grill (with the top vent open for a charcoal grill) and cook for 15 minutes.
• Using tongs and a wad of paper towels, rotate the chicken 90 degrees so the wings are at 6 and 12 o’clock.
• Continue cooking and turning the chicken at 15-minute intervals until the thickest part of the thigh registers 170 to 175 degrees, 1 hour to 1¼ hours longer.

Finish and serve:

• With a large wad of paper towels in each hand, transfer the chicken and the can to a clean bowl, keeping the can upright; let rest for 15 minutes (do not discard the paper towels).
• Using the wads of paper towels, carefully lift the chicken off of the can and onto a cutting board.
• Discard the can.
• Carve the chicken, transfer to a platter, and serve.