Actually, Unix was made available only under closed-source license (most notably as "Unix System V" and its commercial derivatives, including AIX and Solaris). This lead to, among other things, a nasty lawsuit against the University of California at Berkeley, who eventually
did make their BSD Unix variant publicly available, after carefully excising most of the AT&T-copyrighted code.
Wikipedia has some information on the relevant history. As usual, treat with skepticism, but it will confirm the basics:
on System V: http://en.wikipedia.org/wiki/UNIX_System_V
on BSD: http://en.wikipedia.org/wiki/Berkeley_Software_Distribution
