Based on the slap-fighting that’s been going on about this, my best guess is, the chicken got here pre-Polynesian, then continued to be bred and eaten separately from the initial introduction(s); as Heyerdahl suspected, the first colonization of (at least) the eastern Pacific Islands such as Easter Island came from South America, with the Polynesians arriving later (and I doubt his view is controversial any longer, apart from some knee-jerk hidebound dumbasses who just hate Heyerdahl); the final genetic kick came post-1492.
Chicken Bones Suggest Polynesians Found Americas Before Columbus
By Heather Whipps
04 June 2007
https://www.livescience.com/1567-chicken-bones-suggest-polynesians-americas-columbus.html
Chicken DNA Challenges Theory That Polynesians Beat Europeans to Americas
New finding casts doubt on the theory that Polynesians made it to South America.
6 Minute Read
By Roff Smith, for National Geographic
PUBLISHED March 19, 2014
https://www.nationalgeographic.com/news/2014/3/140318-polynesian-chickens-pacific-migration-america-science/
Ancient DNA Explains How Chickens Got To The Americas
Kristina Killgrove
Senior Contributor
Archaeologist, Writer, Scientist
Nov 23, 2017,10:32am EST
https://www.forbes.com/sites/kristinakillgrove/2017/11/23/ancient-dna-explains-how-chickens-got-to-the-americas/
Thanks.