Does Office 365 work properly on Ubuntu & Chrome OS?

Assuming you are referring to the webmail portion of Office 365, then it doesn't work on Linux + Chrome, but as far as I can tell, there is no reason it shouldn't work.

I think the issue is just with the Linux + Chrome user agent. The webmail works fine under Chrome on Windows and Os X, so I don't see any reason why it shouldn't be able to work fine under Linux. Microsoft most likely "forgot" to include the user agent for the Linux + Chrome combo.

Update:
Got this working on Linux using this user agent spoofer extension, http://spoofer-extension.appspot.com/.

It doesn't work on the built in Windows Chrome 13 user agent, but if you use this user agent , taken from this site, Mozilla/5.0 (Windows NT 5.2; WOW64) AppleWebKit/535.7 (KHTML, like Gecko) Chrome/16.0.912.63 Safari/535.7 It should work.

Note that you may have to logout and log back in for the user agent to be properly reread.

Sorry, but the answer is no. Here are the system requirements:

http://www.microsoft.com/en-us/office365/system-requirements.aspx#fbid=DEOG7U8bNvf