The etymology suggests that you should pronounce it "tree". The argument for pronouncing it "try" is to avoid creating a homophone with the other (more popular) data structure. I would pronounce it "try", but honestly it doesn't come up in conversation as much as I would like.
I actually pronounce it "tree-eye", even though that's all sorts of incorrect.
Phonetically, it should be 'try,' but I don't know how it is pronounced usually.