The Declaration of Independence maintains that:
We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable rights, that among these are Life, Liberty, and the pursuit of Happiness.
If what is meant by this is that people should have the right not to be murdered, their persons and legitimately owned property should not be invaded, and that they may pursue happiness in any way they wish as long as they do not thereby violate the equal rights of all others to do the same, this is perfectly compatible with libertarianism, the philosophy based on homesteading, personal and property rights, the non-aggression axiom, contract, and laissez faire capitalism.
Unfortunately, however, the doctrine of inalienability as construed by many is very different from this. So much so, I shall argue, that it is almost diametrically opposed to the libertarian notion of private property and free enterprise.