First, a disclaimer. As your mom probably told you 6,784 times as a kid, chicken fighting in the pool is a potentially dangerous activity. Necks have been sprained, pool water inhaled, and more than one bikini top has been, um, compromised. That said, it's still a classic.
A chicken fight in the pool is like double-decker wrestling. There are two teams consisting of two people each. Each team has a "bottom" and a "top." The "top" climbs onto the "bottom's" shoulders. The two "top" people are the only ones who actively fight. The object is to knock your opponent into the water, either by toppling just the "top" or both "top" and "bottom" together.
As with any great sporting tradition, there are variations on the rules. Most chicken fighters outlaw scratching, hair pulling, punching, biting or other nasty behavior. Some don't. Some chicken fighters believe the game is won when any part of the "top" touches the water. Others wait for full-body immersion. In some pools, the "bottoms" are allowed to grapple as well. All is fair in love, war and water wrestling.