Chittell was born in Aldershot, Hampshire. His father served in the Indian Army, and on leaving school Chittell intended to join the Royal Navy, but instead, he became a model. His first acting stint was in 1964, with the National Theatre, at Chichester Festival Theatre, in Peter Shaffer's The Royal Hunt of the Sun. He appeared as Potter in the 1967 film To Sir, with Love. In 1968 he appeared as a Trooper in The Charge of the Light Brigade, and made an uncredited appearance in If.... . This was followed by a starring role as one of the Freewheelers, made as an action/adventure children's serial by Southern Television between 1968 and 1973. He also acted for two seasons in the 1970s science fiction TV drama The Tomorrow People.

His other film appearances included roles in The Beast in the Cellar (1970), The Weekend Murders (1970), The Raging Moon (1971), The Last Valley (1971), Erotic Inferno (1975), Golden Rendezvous (1977), Zulu Dawn (1979) and Game for Vultures (1979). He also appeared in a number of Swedish sex films in the 1970s including Swedish Sex Games (aka The Intruders and Let Us Play Sex) in 1975 (which also featured a young Stellan Skarsgård), and Sex in Sweden and Practice Makes Perfect (aka Girl on Her Knees) in 1977.

In 1972, Chittell also appeared in the untransmitted Doomwatch episode "Sex and Violence", playing a character named "Dick Burns", widely believed to be a parody of Cliff Richard and Richard's part in the Nationwide Festival of Light. The "Sex and Violence" episode was included as part of the Doomwatch DVD box set release in April 2016.

Chris also played the character "Junior" in 7 episodes of the 2nd series of Tucker's Luck. (1984)

Chittell has also been the proud recipient of the title of 'Chieftain of the Games' on various occasions, with his most recent being on 11 June 2016 when he presided over the Bearsden and Milngavie Highland Games, as well as taking part in the Clyde Arrows Archery Club '2 End Challenge', scoring 51 points out of a possible 60 and finishing third overall.