As others have said here, the name of regular tea (without spices, etc.) in India is not "chai tea" but just "chai" (in Hindi). "Chai tea" would be like saying "tea tea" (although in two different languages (Hindi and English) in the same two-word phrase), so is redundant. I've had American friends and colleagues who made the same mistake.

From Google Translate (and listen to the sounds via the speaker button - when available):

Hindi:

https://translate.google.com/#view=home&op=translate&sl=en&t...

Marathi:

https://translate.google.com/#view=home&op=translate&sl=en&t...

Tamil (but I've never heard anyone call it that, may be the formal name, I've always heard it called "tea" (as in English) in Tamil:

https://translate.google.com/#view=home&op=translate&sl=en&t...

Gujarati:

https://translate.google.com/#view=home&op=translate&sl=en&t...

Malayalam:

https://translate.google.com/#view=home&op=translate&sl=en&t...

and so on ...