Qualcomm among other ARM vendors have been interested in building the Linux kernel with LLVM/Clang. It's possible to build kernels with this alternative open-source C/C++ compiler, but out-of-tree patches are currently required to the Linux kernel and not everything works smoothly. There's a long TODO list until everything is polished and LLVM/Clang becomes a first-class compiler for the Linux kernel, but the effort was formalized last year with the LLVMLinux project that is hosted by the Linux Foundation.
Among the reasons people continue to be interested in using Clang over GCC is the cleaner and easier to work with code-base of the compiler, compilation times are often faster while using less RAM, there's an assortment of static analysis tools and other useful benefits over GCC, and the compiler is under a BSD-style license.
Developers also are pushing the Linux kernel -- and other key software packages -- through Clang since it leads to more portable code by pushing it through more compilers. Among the challenges that the LLVM Linux project has faced is GCC defaulting to using GNU89 of the C language while Clang defaults to GNU99, the kernel using undocumented GCC behavior, unsupported GCC flags, and Kconfig being GCC-specific.
The state of building the Linux kernel with Clang was talked about last month at the Linux Foundation's Embedded Linux Conference 2013. Embedded below is the video of the talk. For those curious about the state of not using GCC to build the Linux kernel, visit the LF project site.
The good news shared during the presentation is that LLVM/Clang 3.3 will likely work "mostly out-of-the-box" for the Linux kernel, albeit patches are still required on the kernel side. (Right now about four patches are require to upstream LLVM/Clang for x86_64 Linux support.)
Slides of the ELC 2013 presentation can be found on Google Docs.