Born in Milwaukee, he graduated from Whitefish Bay High School before attending the University of Pennsylvania, where he was the president of Mask & Wig, the nation's oldest all-male collegiate musical comedy troupe.
Short, dark, amiable, curly-haired character actor best known on the Broadway stage for playing the lead role of the Baker in the original production of "Into the Woods" by Stephen Sondheim.
Enjoyed a long association with musical writer/composer William Finn. Played the lead role of Marvin in Finn's first musical "In Trousers". In its sequels, "March of the Falsettos" and "Falsettoland" he played the co-starring role of Mendel while Michael Rupert took on the lead role of Marvin. Later Chip was featured in another Finn musical playing the bizarre role of a children's show host called Mr. Bungee in "A New Brain" for which he received a Drama Desk nomination.
Among his many Broadway shows were the musicals "Ride the Winds" (his Broadway debut in 1974), "Grand Hotel" (as Otto Kringelein) and "The Boys from Syracuse" (as Dromio of Ephesus). In 2005, Zien played the part of Goran in "Chitty Chitty Bang Bang", and in 2007 came in as the Thenardier replacement in 2007.
Appeared in the critically-heralded movie United 93 (2006) as heroic plane victim Mark Rothenberg which chronicled the 9/11 attacks.