If you're a Unix system administrator, then given you already know shell, the answer is obvious: C. The kernel and all the important tools are written in C. Perl is in many ways, specially when it comes to system admin stuff, just a thin layer over the C libraries anyway. Beside it being a must for a Unix system administrator, knowing C will significantly increase your understanding of Perl. A lot of Perl things will start to make sense once you know C.
I'd say, for a Unix system administrator (and I've been one for over 15 years on a variety of platforms, including Solaris, (old) SunOS, HP-UX, Linux, AIX, and IRIX), shell and C are a must. And another (scripting) language to write your own stuff in, like Perl, Python, Ruby, Rebol, etc, is very useful.
I'd hire someone without Perl knowledge as a Unix system administrator (although knowing Perl would certainly be welcome). I wouldn't hire someone without C knowledge.