Born William McClellan Chapin on December 28, 1943, in Los Angeles, he was the second of three children of Roy Chapin, a bank manager, and Marquerite Alice Barringer, who later became a kind of personal coach for all of her children's acting careers. His sister Lauren later told about alcohol problems and sexual abuse in the troubled family.

Chapin debuted on the screen at the age of only a few weeks, uncredited as Baby Girl in Casanova Brown, 1944, starring Gary Cooper, and just five months later had another uncredited baby role in Marriage Is a Private Affair, starring Lana Turner. He had another bit role in The Cockeyed Miracle in 1946. He started acting professionally in 1951 in a supporting role in the Broadway stage musical Three Wishes for Jamie, which, while passably successful, toured the West Coast in the summer of the same year. After essential changes regarding dramatization of the play and replacements in the original West Coast cast, when the play moved to New York City in early 1952, it finally became a considerable success and earned him the N.Y. Drama Critics Award as the most promising young actor of the year.

This stage success might have earned him his role as the grandson in the 1952 TV adaption of Paul Osborn's 1938 Broadway play, On Borrowed Time at the Celanese Theatre, but his first real screen role he landed just one year later as the "Diaper Manager" Christie Cooper, the lead role of the 1953 family release The Kid from Left Field, starring Dan Dailey, Anne Bancroft and Lloyd Bridges.

Two smaller screen appearances then fell into line, one in a film noir, entitled Naked Alibi, 1954, with Sterling Hayden and Gloria Grahame and another bit role in the famous screen musical There's No Business Like Show Business, again starring Dan Dailey with Donald O'Connor and Marilyn Monroe, before the boy gained his next memorable screen attentions as the young son of historic clergyman Peter Marshall in A Man Called Peter and Victor Mature's screen son in his second film noir: Violent Saturday, both of which were released in 1955. In between he continued to appear in standard television series such as Waterfront, The Millionaire, and My Friend Flicka, and various TV theaters, anthologies and dramas.

When Charles Laughton personally cast Billy Chapin for the role of young John Harper in his 1955 film classic The Night of the Hunter, the boy was already considered an "acting technician" among the child performers of his time. After a private meeting with Billy in his Hollywood home, Laughton told Davis Grubb, the author of the original story: "What I want is a flexible child, and the boy is exactly that." Later, Laughton publicly offered praise especially for "...the strength of [Chapin's] innate ability to understand the construction of a scene, its impact and its importance." Vintage sources claimed that Laughton might find it difficult to direct Chapin, as well as Sally Jane Bruce, who played his younger sister (Pearl Harper), but contemporary sources and rediscovered archival material from the production of The Night of the Hunter prove that, aside from a few intergenerational tiffs, the old man and the boy got along wonderfully, even if, according to these sources, Robert Mitchum, who played the bogus preacher Harry Powell, in fact took over some directing tasks.

It is not known what was the actual reason that Chapin's final big screen appearance came just a year after The Night of the Hunter, as young Jody Burrows in the 1956 B-Western Tension at Table Rock, starring Richard Egan, but from then on his film career declined until he was acting solely on television, where his career eventually ended late in 1959 in an episode of the long-running family series Fury (1955–60).

Though now considered a classic, The Night of the Hunter was a critical and commercial failure when released, "because of its lack of the proper trappings." The film was an inductee in the 1992 National Film Registry list.

Chapin died on December 2, 2016 following a long illness at the age of 72.