Halfway there is still not there, as Zeno would tell you. Easter Island, the furthest outpost of Polynesia, is about 3500km from the South American mainland, without much but open ocean between.

That said, there are some hints of contact between Polynesia and South America. In 2007 a (now) famous paper came out regarding the discovery of chicken bones in Chile which were carbon dated to the pre-Hispanic era. Chickens are not native to the Americas, but were found throughout Polynesia. There's since been some challenges to the original paper, you can find many of them and the responses linked from this particular paper, but the gist is that the carbon dating may actually overlap with Spanish arrival in South America and there has been some question as to the DNA testing as well (i.e., they might not be Polynesian chickens). Right now it's a debate over lab techniques, which is interesting in it's own right, but unfortunately inconclusive for the moment.

The other possible link comes in the form of the sweet potato. It's accepted that sweet potatoes did move from South America to Polynesia in the pre-Columbian era, but the debate is over whether this was through human actions or not. One possible method of dispersal is simply through seed dispersal along ocean currents. Opponents to this theory cite the commonality between Quechua and various Polynesia languages, which is the kind of linguistic pattern to be expected if Quechua speakers had introduced the tuber to Polynesia. So while I'm personally am not entirely convinced by this, I am still inclined to think it a pretty good argument. This paper inclines towards human dispersal and is a good read.

The core problem with both of these proposals is that there is no "smoking gun" giving us undeniable evidence of Polynesians in America or Americans in Polynesia*. With the Norse, the excavation of the settlement of L'Anse aux Meadows in the 1960s showed conclusively their presence, however fleeting, in the Americas. There has been no such equivalent finding on this topic, which is why we are stuck arguing over laboratory techniques and linguistic dispersal.

*^(There's probably a different discussion to be had regarding why the question is always about the former and never about the latter.)