When a group of guys are playing a sport such as pool or darts and one of the guys screws up his shot and then accepts a chance to have a do-over.
Being chick't is not something that you want to have happen to you as the other group of guys will never let you forget it and will tell everyone they see that you have been chick't.
Billy was playing pool and missed a very easy shot. Mark offered to let Billy shoot again. When Billy accepted the do-over and took the shot he then had been chick't.
At this point Billy's man ranking has taken a hard shot and he must turn in his dude card until he is able to chick, ( the root word of course), someone else.