Claire rose to fame as Waverley Harrison (née Wilson) in the New Zealand TV show Shortland Street, from 1994–1995 and 1997–2005 and Aurora Bay in Outrageous Fortune from 2006–2007.
A recurring guest role in Shortland Street followed, which went on to become core cast, with Chitham starring in the show for seven years as Waverly Wilson (later Harrison).
Chitham next appeared as Aurora Bay, in the second and third seasons of Outrageous Fortune - New Zealand's highest rating drama.
Aurora was the longtime love interest of Van West (Antony Starr) - her character died tragically, after being hit by a bus while trying to hide her ex-boyfriend Tyson's (Ben Barrington) stash of drugs.
Having studied in New York and Los Angeles, Chitham has also appeared in a number of stage productions, including Rabbit, by Nina Raine; The Real Thing, by Tom Stoppard; and The Only Child, by Simon Stone.