Why say 'chai tea'?

It's a pleonasm to me, an InE speaker.

Other phrases that seem redundant because the foreign word means the same thing as the English word:

•Gobi desert (Gobi means "desert" in Mongolian.)

•Naan bread (Naan is a type of bread in many countries.)

Chai means "tea" in Hindi, so when we order "chai tea," we're asking for "tea tea," at least that's what it sounds like to someone from India

To non InE speakers, "chai" in chai-tea is a kind of spice rather than the tea.

In America the phrase chai tea has come to mean the particular kind of tea made in the Indian style. (What Americans call chai tea would be more accurately called masala chai ― masala is the mix of spices used to flavor the chai.)

Ref- Is "Chai Tea" Redundant?

I was always under the impression that chai tea referred to a certain blend of tea, usually lightly spiced.

Masala Chai

As opposed to the variety that would usually be drunk in Britain (I can't speak for the US) with milk - and sugar for the heathens - referred to simply as 'Tea'.

English Breakfast Tea

So while you are correct in stating that 'chai' does indeed mean 'tea' in BrE general, everyday use the two are known as referring to specific types of tea.

Many American English speakers understand chai to refer to a way of preparing tea, and for them it is natural to use chai adjectivally. If you understand chai to mean "tea prepared in the Indian manner" then chai tea can strike your ear as pleonastic.

My opinion: Chai (tea) is nothing but rechristening of the Indian chai for the export market under the name of chai tea.

• The "chai tea" usage would be understood but frowned upon in India.

Similar usage-

Numerous United States coffee houses use the term chai latte or chai tea latte for their version to indicate that the steamed milk of a regular latte is mixed with a spiced tea concentrate instead of espresso. (wiki)