Answer
Five times. Sergey Karjakin has represented Russia in the Chess Olympiad on five separate occasions. He made his debut in 2004 at the age of 14, becoming the youngest player to ever compete for Russia in the event. He went on to play in 2006, 2008, 2010, and 2012. In total, he has played 51 games in the Olympiad, winning 33, drawing 14, and losing 4.