Preheat your grill to a steady medium-high heat, aiming for around 375°F to 400°F. Meanwhile, mix salt, pepper, paprika, and garlic powder in a small bowl to create your spice rub.
Pat the chicken dry thoroughly with paper towels, especially the skin, to ensure it crisps up during grilling. Rub the spice mixture all over the chicken, including inside the cavity, to build flavor.
Stuff the cavity with lemon halves, crushed garlic cloves, and thyme sprigs for brightness and aroma. Secure the cavity closed if needed with kitchen twine or toothpicks.
Open the beer can and pour out or drink a small amount to make room. Place the can on a stable surface, then gently lower the chicken onto the can, balancing it upright with legs on the grill rack. The chicken should sit securely on the can.
Brush the chicken skin lightly with oil to promote crispness and golden color. Carefully transfer the chicken with the can onto the preheated grill, positioning it on the cooler side for indirect heat.
Close the grill lid and cook the chicken for about 1 to 1.5 hours, maintaining steady temperature. During cooking, avoid opening the lid frequently to keep the heat consistent, and baste with oil if needed for extra shine.
Check for doneness by inserting a meat thermometer into the thickest part of the thigh; it should read 165°F. The skin should be deeply golden and crackling, with a smoky aroma filling the air.
Use tongs to carefully remove the chicken from the grill, letting it rest for about 10 minutes to allow juices to redistribute. Carefully lift the chicken off the can, placing it on a serving platter.
Slice or serve the chicken whole, enjoying the crispy, crackling skin and juicy, flavorful meat. The smoky aroma and golden appearance make it perfect for a satisfying meal.
