Furnier was born in Detroit at a hospital that carried the nickname "The Butcher's Palace", but, after a stream of illnesses moved to Phoenix, Arizona in his youth. His grandfather, Thurman Furnier, was an ordained Apostle of the Church of Jesus Christ (Bickertonite). Cooper's father, Ether Furnier, was an ordained Elder. Cooper had some distant French Huguenot ancestry; the remainder of his ancestry was English.

Cooper, influenced by British Bands such as The Beatles, The Rolling Stones, The Who, The Kinks and in particular The Yardbirds, formed a number of rock bands in the 1960s, including the Earwigs, The Spiders, and The Nazz. Furnier, upon learning that Todd Rundgren also had a band called The Nazz, changed the band's name to Alice Cooper (the name Alice Cooper is said to have been agreed upon after one of Furnier's Ouija sessions, and learning that he was a reincarnation of a 17th century "witch" of the same name, according to band legend, although Cooper in interviews has said the name actually came out of thin air conjuring an image of "a cute little girl with an axe behind her back"). The classic Alice Cooper group line up consisted of guitarists Michael Bruce and Glen Buxton, bassist Dennis Dunaway, and drummer Neal Smith. After moving to California in 1968, the band enlisted Shep Gordon as their manager, and the band was soon signed to Frank Zappa's label, Straight Records - releasing two competent but outlandish albums, Pretties For You and Easy Action, to a frosty public and critical reception. Warner Brothers then purchased Straight Records from Frank Zappa and Alice Cooper was more highly promoted with this major label.

Although the band incorporated theatrics in their stage act from the outset, a chance case of press misreporting an unfortunate, unrehearsed stage routine involving Alice and a live chicken led to the band changing tack - capitalizing on tabloid sensationalism and creating a new sub-genre, shock rock. Alice claims that the chicken incident was an accident. He says he thought, "Chickens have wings, so they must be able to fly" so when it was on the stage, he threw it out over the crowd, with the intention of having the chicken fly away. But chickens cannot fly, or at least cannot fly particularly well, and it was instead ripped to shreds by the rowdy audience.