Corey Robin has a long post on this, here is one part:
Hayek complied with the dictator’s request. He had his secretary send a draft of what eventually became chapter 17—“A Model Constitution”—of the third volume of Law, Legislation and Liberty. That chapter includes a section on “Emergency Powers,” which defends temporary dictatorships when “the long-run preservation” of a free society is threatened. “Long run” is an elastic phrase, and by free society Hayek doesn’t mean liberal democracy. He has something more particular and peculiar in mind: “that the coercive powers of government are restricted to the enforcement of universal rules of just conduct, and cannot be used for the achievement of particular purposes.” That last phrase is doing a lot of the work here: Hayek believed, for example, that the effort to secure a specific distribution of wealth constituted the pursuit of a particular purpose. So the threats to a free society might not simply come from international or civil war. Nor must they be imminent. As other parts of the text make clear, those threats could just as likely come from creeping social democracy at home. If the visions of Gunnar Myrdal and John Kenneth Galbraith were realized, Hayek writes, it would produce “a wholly rigid economic structure which…only the force of some dictatorial power could break.”
Hayek came away from Chile convinced that an international propaganda campaign had been unfairly waged against the Pinochet regime (and made explicit comparison to the campaign being waged against South Africa’s apartheid regime). He set about to counter that campaign.
He immediately wrote a report lambasting human rights critics of the regime and sought to have it published in the Frankfurter Allgemeine Zeitung. The editor of this market-friendly newspaper refused, fearing that it would brand Hayek as “a second Chile-Strauss.” (Franz Josef Strauss was a right-wing German politician who had visited Chile in 1977 and met with Pinochet. His views were roundly repudiated by both the Social Democrats and the Christian Democrats in Germany.) Hayek was incensed. He broke off all relations with the paper, explaining that if Strauss had indeed been “attacked for his support for Chile he deserves to be congratulated for his courage.”
There is much more at the link.