Richard Smith was born in Cheltenham, England, and his family relocated to Tauranga, New Zealand, in 1951 when his father, an accountant, decided to pursue a career as a sheep farmer. During his time in New Zealand, Smith developed a fascination with horror and science-fiction double features, which he would often watch in nearby Hamilton. This interest in acting was further fueled by his passion for rock and roll music.
In 1964, Smith returned to England, where he initially attempted a career in singing before transitioning to work as a movie stuntman and fringe theater actor. He later changed his name to O'Brien, adopting the surname of his beloved maternal grandmother, to avoid confusion with another Richard Smith.
O'Brien's professional path crossed with director Jim Sharman in 1972, when Sharman cast him in dual roles for the London stage production of "Jesus Christ Superstar". The two collaborated again on a production of Sam Shepard's "The Unseen Hand", during which O'Brien mentioned his idea for a new rock musical, initially titled "They Came from Denton High". Sharman suggested renaming the play "The Rocky Horror Picture Show", and the production opened in June 1973.