A logical route of import into the North American continent would be over the fabled Beiring Straight land bridge from Asia.
While the Mandans are perhaps the most northernmost tribe known to raise chickens, they were also raised by tribes in what is now Latin America. The Inca even developed their own breed, the Aracuna who lay pastel colored eggs, generally light blue or green.
Therefore, I think it is a stretch to say the Mandan didn't get the chickens until about the time of Lewis and Clark. French Canadian trader Sieur de la Verendrye in 1738 visited the Mandan and recorded many of their agricultural practices, including poultry, in his dairy. One crackpot theory at the time even claimed the Mandan were the descendants Prince Madoc and his followers who had emigrated to America from Wales circa 1170 because they were so civilized (i.e. like white people).
As a boy growing up in North Dakota, I can remember reading parts of la Verendrye's dairy (translated into English, of course) getting a real chuckle at how advanced these "savages" were. One particular passage about how they huddled together naked under buffalo robes in their communal earth lodges to keep warm during the winter was particularly memorable. la Verendrye pointed this out, it seemed, not for the interest but to prove that despite all, they weren't quite as advanced as Europeans after all.
Restorer's point that disease immunities were not well developed in native peoples is, I think, quite valid. The gene pools were definitely limited by tribalism, a relatively sparse population and a rural lifestyle which offered limited opportunities to stir the gene pool.