I'm not quite sure when the chariot stopped being used for war in continental Europe, but the last place it was widely used was Britain (and probably Ireland, but we don't really have the details). When Caesar invaded in 55 b.c. he recorded chariots in use, and Tacitus mentions chariots at the battle of Mons Graupius (somewhere in Scotland) in a.d. 84 (chapter 35, in my edition that's page 86).

Edit: just thought I should probably mention the medieval 'war wagon', most notably used by the Hussites, as I have read some old books were it was depicted as being used on the move, a bit like a chariot (or a sort of medieval tank). All the modern research I've read about it however, believes that they were used as mobile fortifications in a laager (which of course is a tactic that survived into the late 19th century in colonial contexts).