The Father David Reddy Chess club meets bi-weekly to play this age-old game. The club also fields a varsity chess team to compete against other high schools in Western New York. Varsity team members are required to be members of the U.S. Chess Federation. This membership is optional for club members. 

The Varsity team has performed well securing multiple Western New York championships over the years. In 2001, they won the City of Buffalo High School Championship for the third year in a row retiring the Aswad Cup to the Bishop Timon-St. Jude High School trophy case. In December 2004 the team finished 1st in the Pennsylvania Junior Olympics hosted in Bradford, Pennsylvania. In 2005 they placed 3rd overall in the New York State Scholastic High School Championship Tournament. The Team won the City of Buffalo High School Championship in 2006, 2007, 2008 & 2009. In 2012, the team placed 1st in WNY, 2nd in NYS and 3rd National. In 2013, they won the NYS Scholastic High School Reserve Championship, placed 2nd in the League Championship in 2015 and won the Sonwil Tournament in 2019.