Some friends of mine were working on a project to make a non-GNU linux distribution (well maybe not actually for distribution) just to see if they could: https://github.com/burke/non-gnu-linux/wiki
I don't think much has happened with it recently, but they were working to build the kernel with icc (the Intel C compiler).
As of a few weeks ago, Gentoo-Bionic is up at https://gitorious.org/gentoo-bionic which is as far as I know the first attempt at a Linux system built with a BSD licensed libc, Bionic being the Andoid libc. All the other glibc alternatives like uclibc tend to also be GPL licensed.
Bionic is missing a fair amount of stuff, as it only has to run a limited subset on Android, but has enough to run much software.
PCC would probably be easier, and it is still open source. Although a BSD-userland Linux would be interesting, I think the GCC compiler has become so widespread that it is almost impossible not to use it (except for Windows, of course). Even the BSDs, which are thoroughly against copyleft licenses, use GCC.
The kernel is pretty closely coupled to the GNU userland. stali[1] is trying to accomplish the same thing. I think they are using utilities/ibraries from OpenBSD. Not sure if they have a working system, though.
I don't think much has happened with it recently, but they were working to build the kernel with icc (the Intel C compiler).