As a teenager, Chris made his debut for Nottingham Forest in unusual circumstances in that he played in the League Cup Final against Liverpool before he had made his league debut. However he was unable to dispossess Peter Shilton from the Forest goal and joined Queen Park Rangers. Norwich signed him for £225,000 in March 1981 where he became a favourite with the Carrow Road crowds. After five years in Canary colours during which he won full England caps, Chris moved to Scottish giants Rangers for £600,000. He made 173 appearances for Rangers and helped them to numerous Scottish trophies.

A return to England followed with a transfer to Sheffield Wednesday. Chris lost his place in the Wednesday first team to Kevin Pressman following a run of poor performances including England's defeats against Norway and the United States. His blunder in the 1993 FA Cup final replay against League Cup winners Arsenal enabled Andy Linighan to score the winner and take the Gunners into the European Cup Winner's Cup. This provided a space in the UEFA Cup which was taken by Norwich City who had finished third in the league. The result being the UEFA Cup victories over Vitesse Arnhem and Bayern Munich.

Chris later spent some time on loan to Reading before travelling west to participate in the inaugural season of the USA's Major League Soccer with the Kansas City Wiz. Signed by Southampton on loan, Chris endured a serious injury soon after his return to England and was unable to impress manager Graeme Souness. Sunderland then signed Chris from the United States Soccer Federation who held his contract in the spring of 1997.

The following summer he joined Burnley as one of the first signings by their new manager Chris Waddle, a former teammate of Woods at Sheffield Wednesday, Sunderland and England. Chris was unable to break into the Burnley first team but was linked in January 1998 with a return to Carrow Road as cover for the injured Andy Marshall. His opportunity at Turf Moor came in March 1998 when first choice keeper Marlon Beresford was sold to Middlesbrough for £500,000.

However in July 1998, Chris and new Burnley manager Stan Ternant agreed to part company and Chris has since joined former Rangers manager Walter Smith at Everton where Chris will be goalkeeping coach. Chris was also been linked with a move to Conference side Barrow who were experiencing a goalkeeping injury crisis. Whilst at Goodison, Chris has played for their reserves (November 1998 vs Stoke) and in friendlies when there have been shortages to the number of keepers available.