China fell under Communist rule in 1949, when Mao Zedong's Chinese Communist Party established the People's Republic of China. Mao formally proclaimed the new state in Beijing on October 1, 1949, after the Communists defeated the Nationalists in the Chinese Civil War.
The conflict pitted Mao's Communists against Chiang Kai-shek's Kuomintang, or Nationalist Party. The Nationalist government retreated to Taiwan, while the Communist government took control of mainland China. This is why the answer is China, although Taiwan followed a separate political path after 1949.
Mao became the founding leader of the People's Republic and remained China's dominant political figure until his death in 1976. His rule included major campaigns such as the Great Leap Forward and the Cultural Revolution, both of which had enormous social and human consequences.
A common mix-up is confusing the 1949 Communist victory with the founding of the Chinese Communist Party, which occurred earlier, in 1921.