[pphysch]

Sure, but "chai tea" is still redundant. I have never used that term and ordered chai in many places without confusion.

[genewitch]

it's redundant at a place that serves chai, but it isn't redundant at a place that does not serve chai, because you're skipping the "what is chai" question from whoever you're querying.

[thesuitonym]

It's redundant in the same way Earl Grey tea is redundant, though.