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has a fairly good claim, as it has changed the least since the split up of proto-Indo-European.
One major problem in answering this question is that some languages aren't recorded until modern times.
Nu Dolls certainly believes so, since they've put together a site chock-full of nothing but these Euro babes in various states of undress as they strip naked for your viewing pleasure.
Looks as though there are a few more languages that are claimed to be "the oldest".
Languages that are isolates, like Basque, Burushaski and Japanese, cause many problems for linguists.
This is assuming you want the oldest European language still spoken here.
I should have specified the Cartagena of Spain rather than calling it Carthage, the name of the city on the North African coast that fought the Romans during the Punic Wars.
Apparently some Phoenicians were in Spain and even left a temple to Melqart for archaeologists to find.