In 2004, Chris re-wrote the lyrics to the Beatles' "Let It Be" to a song about the England football player Wayne Rooney and recorded it in collaboration with the actor Stephen Campbell Moore and a number of other actors and journalists. The song was reprised and re-recorded, with rewritten lyrics, for the 2006 Fifa World Cup and became a hit on YouTube, with 200,000 hits.

Chris passed his Eleven plus exam and attended Tunbridge Wells Grammar School for Boys before moving to the Michael Hall Steiner School in his fourth year. He later attended the Central School of Speech and Drama. In 2005 he completed an evening class at Birkbeck College and was subsequently accepted for a degree course in history, politics and philosophy.

In early 2006, Chris played the role of Captain Leonard in Sharpe's Challenge, starring Sean Bean, while 2007 has seen him in the TV comedy Bonkers, written by Sally Wainwright as well as Petruchio in The Taming of the Shrew at the Wilton's Music Hall. In 2006 he also appeared as Christian in Cyrano de Bergerac at the Royal Exchange Theatre, Manchester. He later appeared in Peter Hall's production of The Portrait of a Lady. He made his West End debut in late 2008 in Lisa Kron's comedy, Well. In 2010 he appeared alongside Judi Dench in Hall's production of A Midsummer Night's Dream at the Rose Theatre, Kingston.

Chris was also cast in Ben Miller's feature-length debut comedy film Huge, which premiered in June 2010. 2011 has seen him appear in two episodes of Silent Witness, whilst also playing one of the leading roles in the National Theatre production of One Man, Two Guvnors alongside James Corden. He appeared in three series of the BBC Three comedy Bluestone 42, about a British bomb disposal detachment in Afghanistan. He also played Dr Richard Truscott in the ITV medical drama series Breathless, set in the 1960s, which ran for one series from October 2013.

From 2014 to 2016, Chris played Prince william in the play King Charles III, appearing in the West End and on Broadway. In May 2017, he appeared in the same role in the BBC Two film adaptation.

February to May 2017 Chris was playing Orsino in a new production of Twelfth Night at the Royal National Theatre. He is due to play Friedrich Engels in Richard Bean and Clive Coleman's new play Young Marx, the opening production at the Bridge Theatre in December 2017.