Born in Zittau, Bindrich became a FIDE Master at the age of 13. He earned his International Master title in 2006 and his grandmaster title a year later. He played in the 2008 Chess Olympiad, held in Dresden, where his German team placed 13th. He has competed in several other prestigious chess events, such as the 2008 Bundesliga and the 2010 Chess Olympiad.