Zambrana Enríquez has won the Bolivian Chess Championship five times between 2002 and 2014. In team competitions, he has represented Bolivia in the Chess Olympiad (1998, 2000, 2002, 2004, 2006, 2008, 2012, 2014), the World Youth U26 Team Chess Championship and the Mercosur Chess Olympiad. He won the individual silver medal on board 3 in the 2000 Chess Olympiad at Instanbul.