While Wine on Android is making progress, Wine on Chrome OS is a much tougher challenge. Long story short, you can't have a fully-working Wine in Chrome OS or Chrome compiled via NaCL. While Chrome OS is Linux-based, the big issue in having the Wine support seems to deal around with Google's sandboxing and not allowing Wine full system access.
For those curious about the state and issues, there's the WineHQ.org NaCl page and a recent mailing list thread about Wine support for Chrome OS. Wine developer Michael Müller had written, "To sum it up: The provided interfaces are not powerful enough to run Wine as a sandboxed plugin. You may disable the sandbox and port some parts of Wine to actually use for example the audio interface or to draw a desktop into a plugin area, but I doubt that someone is actually going to use Chrome without a sandbox. For ChromeOS all this gets even more difficult, because I doubt that you'll even be able to execute Chrome without a sandbox."