What is the basis of Locke's argument that human beings have natural rights? Does Rousseau agree? Why or why not?

Although he was an Enlightenment philosopher, Locke was also a man of God, in the sense that he believed in a higher power who had endowed humans with not only superior intelligence and self-awareness, but also inalienable rights. It is very possible that Locke, like many other Enlightenment philosophers, was a Deist, meaning that he believed in what Descartes termed a "Watchmaker God," one who set the universe in motion but then stepped back and did not intervene in the daily fate of the world that he/she had created. Nevertheless, when Locke sought to make the argument that humans had inalienable rights, he likely looked at how monarchs had justified their own rule, through the "Divine Right of Kings," which he opposed. 

Yet he judged that in order to make the then-extraordinary argument that ordinary people had rights, he would need to draw upon the moral authority of the highest power ("God"), who had imbued humans with these rights. After all, Locke still lived in a very Christian society, and was himself at least outwardly religious, as most scholars and other prominent figures had to be at the time in order to maintain their positions in society. So the most straightforward answer to the question is that Locke claimed that humans were born with certain basic rights as a consequence of their uniqueness, which was understood to be a direct result of being made in "God's image." Yet the term Locke used to describe the the moral authority he sought was "The Law of Nature." Still, Locke argued that God had given human kind this so-called law of nature, and thus it served as the moral backbone of his other contentions.

Rousseau also believed that humans were born free, endowed with certain rights by their “creator,” although he famously observed in the opening of "The Social Contract," that "Men are born free, but everywhere they are in chains." What Rousseau meant by this was that men were indeed born with certain inalienable rights, conferred by God, but that the systems of government, education and commerce of large, modern societies had stripped men of their free will, by damaging their moral compasses and by limiting their freedom of expression, thought action with laws aimed at keeping order. 

Ultimately, both Locke and Rousseau believed that humans were uniquely blessed with God-given rights. Rousseau was more critical of organized religion, education and what he deemed a materialistic society, which turned men against each other and away from their purer, more benevolent natures. At the center of both of these men’s philosophies was the idea that a new system of government could bring out the best nature of man, instead of the worst, and that system needed to derive its power not from an authoritarian ruler, but from the will of the people.