The band formed in 1983, and an early version of the group had Tracii Guns (born Tracy Ulrich) on guitar and W. Axl Rose on vocals. Rose would leave to sing for Rapidfire and Hollywood Rose, before rejoining L.A. Guns, and the group was later renamed Guns N' Roses. However, after a fight with Rose, Tracii Guns left Guns N' Roses and reformed L.A. Guns. (Quite a tangled web, huh?)
L.A. Guns released their first major label record in 1988, and the LP did well, reaching #50 on the charts. However, 1989's Cocked and Loaded did better, and hit #38 on the charts. "The Ballad of Jayne" became the group's only top 40 hit at #33, making the band an official one hit wonder.
While 1991's Hollywood Vampires broke the top 50 on the album charts, the rise of grunge effectively ended any chance of L.A. Guns breaking out. The band has continued as a working band (with a ton of personnel changes) to the present day. In fact, for much of the early 2000's, there were two version of L.A. Guns (one with Tracii Guns and one without). In 2013 Tracii Guns broke up his version of the group, but I believe that the second version is active as of this writing.
Cool trivia fact: "The Ballad of Jayne" is about actress Jayne Mansfield, who was killed in a car accident in 1967.