The Joker became DC's first villain to get an ongoing series with The Joker 1 (May 1975). Despite all the villains pictured on the cover, only Two-Face guest stars in the issue.
Denny O'Neil, Irv Novick and Dick Giordano are the creative team on this issue, which begins in Arkham Asylum. A foreign criminal, Senor Alvarez, breaks Two-Face out of the asylum to aid him in a crime. The Joker sees this, and asks to be released as well, but Alvarez refuses, and Two-Face has no problem leaving him behind. So the Joker breaks out of Arkham on his own, and sets out to mess up the crime that Two-Face is involved in.
Alvarez wants Two-Face to steal a set of double headed doubloons that are on tour in the US from his country. Two-Face agrees, but the Joker bursts in. He sprays Alvarez in the face with acid, but Two-Face gets away, hitting the Joker with a bowl of pears.
The story continues as the two villains fight it out, while Two-Face manages to execute the robbery despite the Joker's efforts to screw things up.
Eventually the two wind up knocking each other out, and both get taken back to Arkham. In a nice twist, the doubloons that Two-Face steals turn out to be counterfeit. Alvarez had stolen the real ones before they ever left his country, and enlisted Two-Face only so that the villain could get the blame for it.
Before this issue, the Joker had last appeared in Brave and the Bold the month before, taking on Batman and Wildcat. Two-Face had last been seen a few months earlier, in Batman, and would return in a few months for a cameo in the Creeper story in 1st Issue Special.