I suspect that if we venture into the streets of an American city and interview random passers-by, fewer than 10% will know that "chai" is a word that already means "tea".
In this case, I would argue that it does. "Sahara" means "desert", but "Sahara Desert" is still the proper name for that place. "Naan" means "bread", but it's also the name we use for the kind of bread originally made by the people who speak the language where "naan" means "bread". Likewise, "chai tea" is a perfectly fine name for tea made in the style of the people whose word for "tea" is "chai". Languages do this all the time.
That’s not a given in many coffee shops. Adding spices makes it “masala chai”, which some sell as a separate drink. Some don’t put spices and call it “chai latte”.
> Masala chai is a popular beverage throughout South Asia, originating in the early modern Indian subcontinent. Chai is made by brewing black tea (usually CTC tea) in milk and water and then sweetening with sugar. Adding aromatic herbs and spices creates masala chai, although chai is often prepared unspiced.[2][3]
It's great to refer to things by their proper names, never mind the corruption that English has adopted.
Still, rude to correct someone for using what's essentially a colloquialism. If enough people use a word 'wrong' then, well, that's a new usage that we can't ignore or get prescriptive about. Because prescriptive usage is from some point of view after all. The Chai tea people have their point of view, and are correct within their community.
Except you're wrong, and this type of construction is extremely common. Take "pine tree" for example. There's nothing "incorrect" about calling it chai tea.
I suspect that if we venture into the streets of an American city and interview random passers-by, fewer than 10% will know that "chai" is a word that already means "tea".