We get our word chai (meaning a specific type of Indian spiced tea) from the Urdu word chay, which meant "tea" in general- so when we say "chai tea", it really means "tea tea". Chay comes from the Mandarin word cha (everything from here on out will also mean "tea", so I won't bother with definitions anymore), and that comes from the Old Chinese word rla. Rla is also the source of the Min Nan Chinese word te, which yielded Malay teh, a word that was picked up by the Dutch when they claimed the East Indies for themselves. Not long after, the English borrowed the word as tea. So, not only is chai tea redundant, but the two words are etymologically connected. It gets way more interesting than that, though: the Old Chinese root rla had amazing spread. As it traveled with the tea, it evolved into words as diverse as Swahili chai, Hausa shayi, Turkish chay, Finnish tee, Japanese ocha, and many more. Almost all modern languages' words for tea are connected by that one word. Fascinating.
Adam Aleksic, a rising sophomore studying linguistics and government at Harvard University, has been described as the internet's sixth most famous etymologist. He also has disturbing interests in politics, vexillology, geography, board games, conlanging, and law.