The answer first.
There is only one way to write Taiji quan correctly, and it’s the way we just typed it: Tai ji quan
Why not Tai “chi”?
- first: Tai “chi” produces a sound that has nothing to do with the Chinese character 极 “ji” . “Chi” has been forced in dictionaries to be the closest sound to “ji” for most of the English-based countries, but it’s not the correct sound. If you say “tai chi” in China, you are basically mixing “tai” with “qi” (of qi gong).
- second: if the sound “chi” was to be the correct one, how would the word “qi” in qi gong sound like…? Qi, as explained here, yes is pronounced “chi”, and must not be confused with “ji” in “Taiji quan”: they are two totally different words, one meaning “air”, the other one meaning “edge, extremity” (same as in Baji quan).
- third: Tai ji quan belongs to Pinyin, the official and worldwide recognized Romanization system for Standard Chinese in mainland China
Why not “chuan”?
Again, “chuan” has been chosen in worldwide dictionaries as the closest sound to “quan”, although it’s both written and spelled wrong. Tai ji quan is the correct way (see Pinyin).