How long should it take to bbq half a chicken?
Way too many variables. If you knew how warm the chicken was before cooking, how hot the cooking area is (and whether that will change during the cooking time), how thick the chicken is, whether you're cooking white or dark meat, and more, you might be able to make a good guess.

I would not recommend cooking just thawed, thick pieces of chicken on an uncovered grill. Too easy to make it hard on the outside and dry on the inside.

I wouldn't estimate lower than 20 minutes, but it will almost certainly be longer.

Edit: Here's a "Good Eats" video about doing chicken on a grill. http://www.youtube.com/watch?v=aAvy4YksJgM&amp;feature=related It's better to go ahead and cut the chicken up the rest of the way for grilling so that each type and size of meat can be on it's own cooking schedule.