yeah... I can type in Chinese only with my Chromebook laptop. I don't have a working Chinese input on my windows laptop (which is what I'm using now) because of some crush (and here's no point to fix it since this is a school laptop).
@断片化的记忆 you may use Sogou Pinyin input for Linux. Like Android, Chrome Os is so modified that you barely feel its linux nature. Chinese input methods, include pinyin, zhuyin, canjie and etc, are well locally supported by ChromeOS.