Take Out the Trash Day - S1-E13
Corrected entry: In this episode, presumably set in early 2000, Leo claims that he hasn't had a drink in six and a half years - which would suggest late 1993 - but this is contradicted twice in later episodes. In the Season 3 episode Bartlet for America, we see a flashback to the early stages of the Bartlet presidential campaign (which would be at the latest 1997) in which Leo is seen being in a drunken state. Later, in the Season 6 episode "Ninety Miles Away", there is a flashback to 1995 in Cuba where Leo is again seen in an inebriated state, where he was assisted by Kate Harper.
Correction: Leo explains, in the episode "Bartlet for America" that, only Josh and the President know about his relapse during the campaign, saying "I went to rehab and my friends embraced me when I got out. You relapse, it's not like that - 'get away from me' - that's what it's like." This is most likely the reason he told Karen Larson he hadn't had a drink since coming out of rehab.