Chickens are derived from the jungle fowl of another continent... not North America.
There is no telling where they got the chickens. The Bearing land bridge theorists would probably argue from Asia many centuries before. Some of the same theorists will tell you that the camel and horse originated in the American continent tens of thousands of years before, but died out when the climate warmed and dried.
Who knows? And that's not really my point. My point is that there is a lot more genetic diversity in Native American peoples than many so-called scholars like to believe . . . including evidence of transoceanic travel and settlement by people of mainly Caucasian origin. Just google "Kennewick Man" for some interesting reading.