I'm planning to travel round Argentina and Chile and find a TEFL job in the process. I'm a native English speaker, have a CELTA certificate plus one year's experience as an English teacher, but the jobs I see on the internet always seem to mention a universtity degree which I don't have. Would I be wasting my time looking for a TEFL job in Argentina or Chile?

No, you wouldn't be wasting your time. The best way to find a job there is to just go, then find one when you're there.

I imagine that it would be much the same in Argentina and Chile as it is here in Thailand. Officially you're supposed to hold a teaching degree or an unrelated degree and an ESL/EFL cert. like you have to get a job in Thailand, but the reality is very different. Even back-packers with no qualifications what so ever still manage to land themselves teaching jobs in Thailand.

Just go, and have a good time while you're there!