Can I Install Java on a Chromebook?
No. Google has chosen not to include support for Java in Chrome OS. For the average user, installing Java or the Java browser plugin is not possible.
Similarly to Apple’s decision not to allow Java apps on the iPhone, Google does not support Java or the Java plugin for Chromebooks. They do support the Java plugin for Chrome on Windows, Mac and Linux desktops, so including support for Java on a Chromebook doesn’t seem to be a real technical problem but more likely a clue to how Google really feels about Java on websites. Google is a huge supporter of HTML5 and want to encourage developers to write web apps for HTML5 web standards instead of Java or Flash (although, ironically, they do support Flash on Chromebooks).
Now, if you REALLY need Java to run on a Chromebook, there are ways, but not without installing another operating system like Ubuntu via Crouton. This is not recommended for anyone but real power users and Linux geeks! You could also access an existing computer with Java installed and use your Java apps that way. For example, use Chrome Remote Desktop to access a Mac, Linux or Windows computer and do your Java work (or play) from there.