Yes, Chaing-Kai-shek was defeated in mainland China. I didn't phrase my comment well. Sorry.
From what I've read, Taiwan was originally settled by people of Polynesian/Malay descent. When the Dutch took over in the 1620's, they imported Chinese from the mainland as workers. These Chinese intermarried with the aboriginal population, and their descendants are the modern day Taiwanese.
When the Dutch were driven off, the Manchu emperors tried to extend their influence over the island, but were not very successful, with continuous clashes between the locals and the officials from the mainland. It wasn't until the late 1880's that the Manchu Imperial Authorities declared Taiwan to be a province of China. When Japan defeated China in the Sino-Japanese war in 1895, China ceded Taiwan to Japan "in perpetuity".
So Japan ruled Taiwan for 50 years, but when Japan was defeated in WW2, the Allied powers agreed to let Chaing "temporarily" occupy Taiwan in 1945, as their agent. In 1949, after losing to the communists, Chaing re-established the remainder of his government permanently in Taiwan. In 1951-1952, the San Francisco Peace Treaty formally concluded the war with Japan, and the treaty allowed for Taiwan's status to be determined by the principles of the UN. Basically it meant that the Taiwanese people should determine their own fate.
So I will clarify my comment. I think the Taiwanese people should be the ones determining their fate. If they choose independence, it should be honored. If they choose to join with China, that should be honored also.
-CM