John Hawks points me to this story in The New York Times about research to be published in PNAS. Basically the researchers found that chickens buried in south-central Chile about a century before the Spanish contact with the New World were genetically most similar to those from Polynesia. This is a pretty obvious case for pre-European contact between Old and New World peoples. Frankly, on a priori grounds this is a no brainer, if Polynesians could make to Easter Island it seems implausible that continental South America would be too far. Also, there is historical documentation which suggests that the Incas used chickens in their religious rituals when the Spanish first entered their territory. One could hypothesize that the chickens had spread via cultural diffusion from the region of first contact in the Caribbean, but these genetic data puts that theory to rest (another case where genetic data clarifies a historical question). There is no real data which suggests that Polynesians had any demographic impact upon the New World. This makes sense, the effective population of th sources of colonization would have been relatively small compared to target population, so the expeditions would have been tiny. Genetic drift over the past few centuries might have inundated the small signal of intermarriage on the neutral markers which have been assayed in this region, but I wouldn't be surprised if meta-population dynamics are at work in explaining why we might not detect a signature of admixture (south-central Chile might have been subject to pre-state social processes which involved more deme vs. deme competition and extinction). Imagine that the Polynesians intermarried with a particular tribe, it maybe that that tribe was exterminated in internecine warfare rather soon after the initial hybridization event, though the utilization of chickens had already spread to hostile neighbors via furtive contacts. Finally, the spread of chickens seems to be pretty analogous to the introgression story. Chickens jumped the population barrier because they were a positively selected cultural character.