There have been ideas floated about pre-Columbian South American contacts with eastern people since Betty Meggers et al., in the 1960s, hypothesized a 5,000 year old connection between Jomon pottery from Japan and pottery styles of the Valdivia culture of coastal Ecuador. The connection between the pottery styles never panned out, and it has since been rejected. However, more recent research has resulted in evidence of contact between Polynesian people and residents of the west coast of South America about 1,000 years ago.

The evidence, surprisingly enough, is in the form of sweet potatoes. Sweet potatoes are native to South America but not the Polynesian Islands or points east. The specific species of sweet potato starts showing up in the South Pacific, and points east, about a thousand years ago. Sweet Potatoes make it all the way to New Zealand and the names used for them there - kumal, kuumara and comal - are almost exactly the same as used by indigenous people in South America. Throughout the South Pacific, the specific type of South American potato is known as kummara or a close variant. You can read about it here. The NPR article is pretty brief so here is the peer reviewed article about it.

Other than the South American sweet-potato connection with Oceania, no other contacts between prehistoric old and new worlds have been convincingly documented.

Edit: straightened out my dates.