Chiang's Facebook page on Friday did not contain any specific threats but included a rant against school officials.
"I think TAS administrators are a group of ugly, balding and used-up white people," a posting said. "They are quite retarded."
Taiwanese media report that starting in August, Chiang used his Facebook page and email to threaten to kill staff and students at the school. A former teacher said Chiang is 23 and was expelled from TAS about six years ago after getting into an altercation with a fellow student.
The former teacher spoke on condition of anonymity because she feared retribution from school authorities.
Taipei American School has 2,600 students, many the well-heeled scions of Taiwanese business and political leaders who possess foreign passports.
Chiang Kai-shek fled to Taiwan in 1949 after losing the Chinese civil war to Communists on the mainland, and he ruled the island until his death in 1975. One of his successors was son Chiang Ching-kuo, Chiang You-ching's grandfather.