Root Beer-Can Chicken

This is a family-friendly version of beer-can chicken, in which we use an open can of root beer to bake a whole bird on the grill. The liquid inside the jar moisturizes, making the meat juicy and tender. Finish your meal with grilled red potatoes and a sweet and tart broccoli salad.
Prepare the grill for indirect cooking, preheat on one side to medium.Combine the first 7 ingredients and 1/2 teaspoon of salt in a small bowl.Open both root beer cans; pour 18 ounces into a small saucepan. Set the remaining root beer (in the jar) aside. Bring 18 ounces of root beer to a boil. Cook until reduced to 1/3 cup (about 20 minutes). Remove from heat. Add the remaining 1/4 teaspoon salt, butter, and vinegar, stirring until smooth.Rub the chicken evenly with the paprika mixture. Holding the chicken vertically with the cavity facing down, insert the remaining open root beer jar into the cavity. Place the chicken on the unheated side of the grill. Spread the legs apart to form a chicken stand. Cover and grill for 1 hour and 30 minutes, or until a meat thermometer inserted in the meaty part of the thigh reads 160 °, drizzling the chicken with sauce every 20 minutes.Lift the chicken slightly with a pair of tongs; place the spatula under the jar. Carefully remove the chicken and jar from the grill; place on a cutting board. Let stand for 10 minutes. Gently lift the chicken using tongs or insulated rubber gloves; gently turn the jar over and remove from the cavity. Discard the jar. Cut up the chicken.