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.

Since December 2010, Chris has also coached the United States national team goalkeepers.

On 1st July 2013, Woods followed David Moyes from Everton to Manchester United along with assistant manager Steve Round and coach Jimmy Unsworth.

Following Moyes sacking in April 2014 and the appointment of Louis Van Gaal as United's new manager on 19th May 2014, rumours circulated that Woods had no future at Old Trafford. Van Gaal appointed Frans Hoek as United's goalkeeping coach. Woods was at the 2014 World Cup in Brazil with the USA National Team.

After leaving Manchester United in the summer of 2014, Woods focussed on the USA team until 15th June 2015 when he became the goalkeeping coach at West Ham United under new manager Slaven Bilic. He left the role in May 2018.

On 24th August 2021 it was reported that Woods had joined Steve Clarke's coaching team for the Scottish national team.