Chambers' career began at Grove Vale F.C in 1996, before signing for West Bromwich Albion as an apprentice in July 1997.After progressing through Albion's youth system, he turned professional in January 1999.
In the 1998/99 season Adam and his brother James became the first twins to represent England at any level when they appeared together during the World Youth Tournament in Nigeria.
Adam made his first team debut for Albion on 9 September 2000, coming on as a substitute in a 0–0 draw away at Stockport County.
Adam played more than 60 times for Albion, but often struggled to hold down a first team place. During the 2003/04 season, he went on loan to Sheffield Wednesday. In February 2005, his contract at Albion was terminated by mutual consent, and he briefly joined Kidderminster Harriers.
After Injury ruled him out of the 2005–06 season completely Adam signed a one-year contract with Leyton Orient at the beginning of the 2006/07 campaign. On 5 February 2007, Chambers signed a two and a half year contract which keeps him at the club until the end of the 2008–09 season. Chambers scored his first goal for 15 months in the 2–1 defeat to Southend United on December 28, 2009 with a 20 yard volley.
After being released by the Orient at the end of the 2010/11 season, Adam signed for Walsall in July 2011 on a one-year deal, with an option of a further year. Adam made a sucessful start to his Saddlers career by scoring on his competitive debut against former club Orient with a stunning top corner drive.
Adam has gone on to establish himself as a first team regular at the club and is many supporters' first name on the team-sheet.