Until now we have seen x86 Intel and ARM powered chromebooks but rumors are brewing that a laptop of netbook with MIPS will be launched soon. MIPS is under control of Imagination Technologies and its developers are working to release chromebook with MIPS architecture.
Currently we have no official information or confirmation from the company but the latest update of coreboot suggests that MIPS support is added to chromium OS.
The developers of MIPS are confident that their processors can outperform ARM processors without any increase in price tag. Also it shall be noted that Imagination Technologies has not yet announced the next generation of its high-end chip-based MIPS64 cores that rivals of the ARM Cortex A57 and Qualcomm Core Kryo. These CPUs have been developed for smartphones but could be used for Chromebook with higher performance.