This is from the 2004 Libertarian Party Platform (under Individual Rights).
“We call for the elimination of all restrictions on immigration, the abolition of the Immigration and Naturalization Service and the Border Patrol, and a declaration of full amnesty for all people who have entered the country illegally.”
Libertarians get a lot right - a whole lot. But immigration isn't one of them. They ignore the unlevel playing field that libertarian theory presumes to be non-existent. But it's only non-existent in a completely libertarian world - otherwise it's presumption is dangerously naive. That's why libertarianism only works best internally, where a level playing field can at least be theoretically created. Against international problems though, it would lead to slaughter.