In The Fatal Conceit, Hayek tries to explain how the "extended order" came into being, i.e. the global civilization in which we now live. It is fair to say that, according to Hayek, capitalism is what has allowed the extended order to come into being and continue to exist. Without the spontaneous processes of cultural evolution (see my previous blog post on the matter) human life would never be able to thrive in such large groups.
However, Hayek had trouble with the word "capitalism."