One of the perennial pre-Columbian contact theories involves ancient visits by the Chinese to America. This is made plausible for several reasons. First of all, the voyage around the great circle route across the Pacific is facilitated by almost constant visibility of land and prevailing sea-currents. China had advanced maritime technology long before the European age of discovery, and historically were known to have taken long sea voyages to distant ports such as Africa, Arabia and India before Vasco de Gamma set sail. And lastly, there are suggestive Chinese accounts of lands far to the East in their chronicles. This book, written in the 19th century by Charles Leland, examines these records, and also reviews some of the evidence for such contacts.
This has remained a popular hypothesis to the current day. For instance, 1421 :The Year China Discovered America, by Gavin Menzies, and Voyages of the Pyramid Builders, by Jeremy P. Tarcher, are two recent books which propose pre-Columbian voyages from China to the New World. However, Leland's Fusang explored this concept over a century ago, and is required reading if you have any interest in this topic.