As an Egyptian, maybe a little over a thousand years, as that’s when most people started speaking Arabic, though depending on where exactly I am I could luck into an Arab community, in which case I’d last until maybe 1200 years go. Before that it was Coptic and I don’t speak a lick of that.

As an American, I’ll include England, in which case, it’s really longer than you’d think before you’d need a translator. Shakespeare gets a lot of guff, but it’s important to remember he was writing in a elevated register and everyday vocabulary would be a little easier to parse. The accent itself wouldn’t be that bad, a rhotic accent that hits my American ears with a combination of Cockney, West Country, and a sort of indistinct Irishness, but as David Crystal points out, because it predates much of the geographic splintering caused by the British Isles diaspora in the 17th through 19th centuries, Anglophones from all across the world often find some aspect of it that feels familiar.

Now, Chaucer was before the Great Vowel Shift really got going, so it’s tougher, but I think if you found a motivated conversationalist, you’d adjust quickly enough to function without needing a formal translator. Chaucer influenced written English quite a bit, and he was speaking with a London accent that contributed more to current dialects than some others, so it might be impractical to go much earlier than him. The bigger issues than language itself would really be cultural context and general knowledge of the time and place.

https://en.wikipedia.org/wiki/Mikael_Agricola

Agricola’s Finnish is reasonably understandable, so about as far as the records go. 1500’s or so.

Maybe some linguist might have ideas about earlier history, but that’s my guess.