The United States supported the Republic of China lead by Kuomintang. In this Civil War, this group was facing off against the Communist Party of China. Considering when this war happened (1920-1950's), the US gave strong support to the Republic of China because America was worried about the spread of communism.
Almost immediately after World War II, America adopted a foreign policy of containment. This concept was focused around stopping the spread of communism all over the world. The US was worried that if communism would spread to one country, that it would spread to neighbor countries as well (also known as the domino effect).
Considering the US's long standing economic relationship with China, this entire country falling into the hands of communism would be extremely bad. This is why they support this group throughout the Chinese Civil War.
