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Pat chicken dry with paper towels. For extra crispy skin, refrigerate uncovered for 1 hour.
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Mix salt, pepper, paprika, garlic powder, thyme, and lime zest.
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Rub the chicken lightly with oil, then season generously with the spice mix, getting under the skin where possible.
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Open the beer and pour out (or sip) half. Drop a pinch of the spice mix and a slice of lime into the can.
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Place the can in a chicken stand/holder, then carefully lower the chicken over the can so it sits upright.
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Preheat grill to medium (around 375°F) with indirect heat.
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Grill for 1–1 ¼ hours, or until breast reaches 165°F and thighs 180°F.
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Remove chicken from the grill, tent with foil, and rest for 10 minutes before carving.