No.

I'm not sure what else to say about such a bizarre claim, but it has a simple answer. Cortes encountered a Mesoamerica where a small triple alliance of powerful central city states (Tenochtitlan, Texcoco, Tlacopan) located around the valley of Mexico dominated military affairs in the region. The alliance was less than a hundred years old, and their dominance over the region was the result of (what else?) a series of wars. The subjugated cities were unhappy enough to (in some crucial cases) side with Cortes against the triple alliance. (I suspect they saw it as Cortes siding with them!) The political situation in the Andes, around what we call the Inca empire, was not much different. Other parts of the Americas were less densely inhabited, with less powerful and less sedentary states, but they certainly weren't free from warfare.

Nobody played the game of interstate warfare quite as diligently or on quite the same scale as Europeans, at least by the time of Columbus, but there is no inhabited part of the world where there has been a thousand years of peace. At least none that I've ever heard of.