A reference to Family Guy, in which protagonist Peter Griffin is chatting away or in the middle of some sort of mundane task, and a chicken (who had a dispute with Peter in an earlier episode) attacks him and a long fight scene ensues only for Peter to return after the fight, battered and bruised to his conversation or task as if the fight had never occurred. Sometimes these "occurrences" happen in real life, perhaps you and your friend have an argument or you have a 3:00am brawl with your neighbors, yet in the end you make up and things get back to normal, as if it never happened... hence the term "Chicken Fight".
Girl: "Hey how is your brother feeling?"
Boy: "A lot better, he's made a full recovery. It's almost like he never got sick."
Girl: "Wow, I guess he and his cold were having a chicken fight."