Chapman’s first notable band was the Welsh outfit Universe. Chapman then joined Skid Row in December 1971 replacing Gary Moore as guitarist. His tenure was fairly short and only lasted until July 1972. His next band was Kimla Taz, with whom he was guitarist from December 1972 to May 1974.
Chapman first joined UFO in 1974 as a second guitarist to augment their live sound having answered an advert in UK's music paper, Melody Maker. He auditioned at the Unity Theatre in London. Although Chapman did not record an album during this period, he did join in time to tour and promote the Phenomenon album. However, he can be heard with the band on several tracks on the BBC live sessions album that was released retrospectively. He left UFO in January 1975 due to personal differences with the band, and went on to form Lone Star, where he remained until June 1978.
In 1977, he filled in for Michael Schenker in UFO when they were on tour with Rush in the United States during one of the German guitarist's absences.
After resuming with Lone Star following the tour, Chapman later rejoined UFO in December 1978 on a full-time basis after Schenker and UFO parted company. By this time UFO were an international success, and were about to release their live album, Strangers in the Night which would increase their profile even further. Chapman is acknowledged on the album.
Chapman recorded his first album with UFO – No Place To Run - with ex-Beatles producer George Martin; which was released in January 1980. UFO undertook a tour to promote it culminating in a five night sell out at London’s Hammersmith Odeon.
Chapman remained in UFO until 1983 and played on another three albums, The Wild, The Willing And The Innocent (1981); Mechanix (1982); and Making Contact. In 1983, after numerous line-up changes UFO decided to call it a day and the tour was promoted as a farewell tour (although they subsequently reformed the following year). UFO released a compilation album later that year incorporating songs featuring various of their members in other bands. Chapman was represented by a Lone Star song. The album was completed by several songs recorded live on the farewell tour.
After the tour, Chapman went to Florida, United States to form a new band DOA. He later hooked up with former UFO band member Pete Way in Waysted and recorded the albums The Good the Bad the Waysted and Save your Prayers. After this Chapman founded Ghost in 1993, fronted by another Welshman, Carl Sentance.
In 1993, Chapman was lined-up as the guitarist for a reformed UFO, but Michael Schenker was employed instead.
Chapman released an album, Anthology Volume One, on his own Paul Chapman Enterprises label, which covered his career from Lonestar through to Ghost. A solo instrumental track, "The Bells of Berlin" appeared as part of the December 2000 archive Waysted collection Your Prayers Are Saved.
He played on a Nazareth tribute album released in 2001, Another Hair Of The Dog, on two tracks "This Flight Tonight" and "Let Me Be Your Dog".
His next appearance was in late 2002, when he guested with former Virgin Steele guitarist Jack Starr's new band project, Jack Starr and the Guardians of the Flame, for the February 2003 album, Under A Savage Sky. Following this Chapman and Pete Way reformed Waysted along with original singer Fin. After completing a new album Chapman resigned from the band in November 2004.
Nothing was heard from Chapman (he became a music instructor at Florida Discount Music in Melbourne, Florida) until May 2006, when he announced he was planning to re-record classic UFO songs. He enlisted the help of Robin McAuley who sang on versions of "No Place To Run", "Wild, Willing & Innocent" and "The Writer" cut at Garudio Studios in Palm Bay. The project has yet to see the light of day.
In July 2006, Chapman joined the American southern rock band Gator Country, a seasoned collection of Molly Hatchet veterans due to the passing of the original Molly Hatchet guitarist Duane Roland.
Currently, Chapman teaches music one-on-one at his studio in downtown Melbourne, Florida.