Of course, since 1949, in case you missed the news. However, TW is political for the "unity of the motherland". China claimed South China Sea probably around the same time too, but IMO, it aimed for natural resource instead.
Actually, Taiwan was the first country to claim the disputed territory (around 1949 IIRC), so we can't even blame China for starting this one. However China certainly did latch hard onto the Taiwanese claim.
TW is Republic of China, so it is some China anyways...