Serve up something everyone will enjoy, our delicious Drunken Chicken recipe thats flavored with amber beer, garlic, jalapeo pepper and more. Beer Butt Chicken, Drunken Chicken, or Beer Can Chicken no matter what you call this chicken cooked on a beer can, this is a delicious way to barbecue a whole chicken. This chicken is the juiciest cooked chicken you will ever try I picked up the McCormick Cookbook for 50 cents in a thrift shop, mainly because this recipe, chicken breasts in a rich rum flavored cream sauce, caught my eye.