After attending New Trier High School in Winnetka, Illinois, he went to Wesleyan University in Middletown, Connecticut in 1954. He majored in drama and was active in fencing, soccer, singing with the glee club and performing in various dramatic performances. He met his future wife, Barbara O' Conner, on a blind date. They were married in 1957 and have two sons, John and Ned. Christopher is also said to be a direct descendent of the American patriot, Paul Revere.

After appearing in a variety of regional productions, Christopher landed roles in a number of off-Broadway productions, most notably The Hostage at One Sheridan Square. His Broadway debut came in Beyond the Fringe, a British revue.

Christopher left the New York stage for Hollywood to attempt to gain work in television, where he guest starred in several well-known series, including: The Andy Griffith Show (he portrayed a new, young doctor scheduling Opie Taylor for a tonsilectomy), Death Valley Days, The Patty Duke Show and The Men from Shiloh. Christopher had recurring roles on Gomer Pyle, U.S.M.C., That Girl and Hogan's Heroes. In 1972, Christopher landed the role of Father Mulcahy in the television series M*A*S*H.

In feature films, Christopher performed in The Fortune Cookie, The Private Navy of Sgt. O'Farrell, The Shakiest Gun in the West, With Six You Get Eggroll and Hearts of the West. He won parts in such telefilms as The Movie Maker, The Perils of Pauline and For the Love of It. The Doris Day film With Six You Get Eggroll is notable for fans of M*A*S*H as Jamie Farr appears along with Christopher five years before the show, both playing hippies.

Christopher devotes much of his spare time to the National Autistic Society because his son Ned is autistic. He has done public service announcements to bring attention to this medical condition. In 1985 he and his wife wrote Mixed Blessings, a book about their experiences raising Ned.

Since M*A*S*H, Christopher has appeared on various series, including Murder, She Wrote. In 1998, Christopher guest-starred in an episode of Mad About You. Christopher has also remained active in the theater, including a tour of the U.S. in the mid-1990s with Jamie Farr doing Neil Simon's The Odd Couple on stage.