The three main reasons they gave were: 1) a functioning free market with rational agents voluntarily exchanging goods and services requires non-desperate individuals who can realistically say "no" to proposed economic exchanges; 2) a guaranteed minimum income would make people more autonomous market participants, as they would feel more free to be entrepreneurs, and to break from more cliquish kinds of safety nets like churches and ethnic groups; and 3) pragmatically, direct cash transfers are the least distorting kind of anti-poverty program, so a minimum income will greatly reduce political pressure for more distorting measures, like restrictions on when you can fire employees.

Here's one place Hayek discusses it, starting at the bottom of p. 54 and continuing through the middle of p. 56: http://books.google.com/books?id=0HzIUyFkwlYC&pg=PA54