If using a charcoal grill, place a 9-by-13-inch disposable aluminum pan in the center of the bottom rack. Light briquettes in a charcoal chimney. When covered with ash, pour into the grill around (not in) the pan; add the top rack. If using a gas grill, place the aluminum pan under the top rack on one side. Heat the side without the pan to medium-high; leave the burner under the pan off.
Pour out half a can of American-style lager, such as Budweiser. In bowl, mix paprika, light brown sugar, garlic powder, onion powder and cayenne. Spoon 1 tbsp. spice mix into can. Rub 2 tsp. spice mix under skin of chicken. Rub chicken with vegetable oil. Sprinkle with salt, pepper and remaining spice mix.
Push the chicken, legs down, over the can. Thread a toothpick through the skin to close the neck opening; this will trap the flavorful steam that comes out of the can as the chicken cooks. Place the chicken on the rack over the aluminum drip pan, using the can and the legs to prop it up.
Cover and grill, rotating halfway through cooking, until an instantread thermometer inserted into the thickest part of the breast registers 160 degrees , about 1 hour.
Transfer the chicken and can to a cutting board; let rest 10 minutes. Using oven mitts (silicone ones work great), steady the chicken with one mitt, and carefully twist the can with the other mitt to release.