Taiwan Relations Act
The Taiwan Relations Act
is an act of the United States Congress
passed in 1979
after the establishment of relations with the People's Republic of China
and the (pro forma) breaking of relations between the United States the Republic of China
by President Jimmy Carter
The act authorizes quasi-diplomatic relations with the ROC government by establishing the American Institute in Taiwan.
- The absence of diplomatic relations or recognition shall not affect the application of the laws of the United States with respect to Taiwan, and the laws of the United States shall apply with respect to Taiwan in the manner that the laws of the United States applied with respect to Taiwan prior to January 1, 1979. 
The act also states that military action against Taiwan by the People's Republic of China would be considered a "grave threat to peace and security in the Western Pacific." The act however does not require the United States to take any action against the PRC in the event of an attack.
See also: Political status of Taiwan, Foreign relations of Taiwan