Let me break it down for you guys. Once upon a time men were nothing more than baboons with large brains. Survival of the fittest meant resources belonged to the strongest. The ones with "private property", in some broad sense of the term, were the ones who could bash in the skulls of any other smart baboons. Eventually, though, some baboons realized that by cooperating with one another, they could increase their chances of fending off any outside threats to their "private property". Thus, the first tribes and hence "governments", again in a broad sense of the term, were born. Eventually these cooperative associations developed to the point where rules were laid out for how each individual's property was to be respected, and hence law and the modern idea of "private property" developed.
So there can be different senses of the term "private property", and we need to be careful about what we're referring to. Some radicals might advocate a return to the baboon-in-the-jungle idea of "private property", but that's clearly a very different sense of private property than modern day civilized notions of private property, which clearly require some form of government.
Now of course, the government can take different forms, and we can dispute the proper form of government. Private property might exist under a totalitarian state, for instance, as long as the leader forces everyone to respect property rights. But it's clear that coercion of some sort is required for there to truly be private property that does not simply fall into the hands of whoever happens to be the strongest.