Or Silkies could have been transported to Central America by the Chinese in the 1400's during a period immense trading and sailing. Because the faction backing the trading fell out of power after the death of Zheng He (the admiral of the treasure ships) China retreated into a xenophobic pattern and walled themselves off. They also destroyed many of the records of what Zheng He did. It is known that he made 7 great voyages in the Indian Ocean and that he reached Africa. But it is possible that is not all because so much of the information on his voyages were destroyed.
This is a decent write up about a bit of research that came out in March. The journalist did a great job of conveying the findings AND getting feedback from previous researchers who found evidence Pre-Columbian contact.... Spoiler Alert - they disagree

When Did Chickens Cross The Pacific Ocean? DNA Shows ‘No Evidence’ Of Pre-Columbian Contact
According to a new study published in the Proceedings of the National Academy of Sciences, ancient Polynesian chickens might not have migrated to South America as some scientists believe. Researchers came to their conclusion after comparing mitochondrial DNA taken from chicken bones from archeological sites in several Pacific islands with DNA taken from 122 feathers from modern chickens in the SouthPacific.
"We were able to re-examine bones used in previous studies that had linked ancient Pacific and South American chickens, suggesting early human contact, and found that some of the results were contaminated with modern chicken DNA, which occurs at trace levels in many laboratory components," Professor Alan Cooper of the University of Adelaide's Australian Centre for Ancient DNA said in a statement. "We were able to show that the ancient chicken DNA provided no evidence of any pre-Columbian contact between these areas."
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My favorite part of the whole affair is Kermit's response. Clearly the wrong birds were sampled!