Mix ketchup, beer, marinade and brown sugar in medium saucepan. Bring to boil on medium-high heat. Reduce heat to medium; cook 5 minutes, stirring occasionally. Reserve 3/4 cup of the barbecue sauce for serving.
Grill chicken over medium heat 20 to 30 minutes or until cooked through, turning occasionally. Brush with remanining barbecue sauce during last 10 minutes of cooking. Serve chicken with reserved barbecue sauce.