Oh, yeah. It's "taiji" officially. But because it's gotten so popular in the west, the westernized misspellings for this abound, and I've been wirting that "taiqi" in English for years. 

Officially it's "taiji", but not everyone knows what that is. 

In the bohemian land of new-agers, it's "taichi" and to everyone else it's "taiqi, taichee, taiqui" and every other possible wrong way of writing it.