You should absolutely learn C. A good knowledge of C is a very valuable asset for all sorts of work, especially on Unix.

Thankfully, C is straightforward to learn. The major concept you need to understand is pointers; once you've done that, there are some syntactic oddities to absorb (typedefs, function pointer syntax, arrays vs. pointers), and you should skim through the standard library (which is tiny compared to Java, or even C++), and you're most of the way there.

In addition to K&R, I've hears that Steele and Harbison's "C: A Reference Manual" is very good, although I haven't read it personally.