This supports adding a Chrome extension for Russian keyboard support using the Mac phonetic keyboard layout. In particular, this is intended to aid compatibility between OS X and Chrome OS.
The Russian (phonetic Mac) keyboard implementation is available seperately here.
Chrome extension design is based on extra-keyboards-for-chrome-os.
According to the Chromium Projects: Modifications you make to the system are not supported by Google, may cause hardware, software or security issues and may void warranty. It appears that the only way to install the keyboard itself is to put the Chrome OS computer into Developer mode, which is not something that the majority of users would/should do.