Finegold was born into a chess family and became a USCF Master at the age of 14. He became a Life Master at 15, Senior Master at 16, and International Master at 20.
Finegold tied for first place in the 1994 (Chicago, IL) and 2007 (Cherry Hill, NJ) U.S. Open Chess Championships. He tied for first (and achieved a Grandmaster norm) in the 2002 World Open (Philadelphia, PA), and also tied for first in the 2005 and 2008 National Open Chess Championships (Las Vegas, NV). He is ranked as one of the top 40 players in the United States on the August 2013 USCF rating list. Finegold has played in nine U.S. Chess Championships: 1994 (Key West, FL), 1999 (Salt Lake City, UT), 2002 (Seattle, WA), 2005 (La Jolla, CA), 2006 (San Diego, CA), 2008 (Tulsa, OK), 2010 (Saint Louis, MO), 2011 (Saint Louis, MO), 2013 (Saint Louis, MO).