I can not make it work nor find an official confirmation of compatibility. Oracle Java 7 plugin works fine with Firefox but fresh Chromium browser installation does not even list it at chrome://plugins
They've dropped NPAPI plugin support in the latest version of Chromium, which means that it can't use the Firefox version of Flash or Java, which is also an NPAPI plugin. It does support PPAPI plugins, though. Flash has a PPAPI version, but Java doesn't, yet.
Chrome browser (not Chromium) still supports NPAPI, though. You can use Oracle Java and flashplugin-installer with it just like you can with Firefox.
Linux NPAPI support is dropped in this and future versions of Chromium, it's not possible to install Java browser plugin until PPAPI implementation of Java plugin is released by Oracle or third party.
Current version of NPAPI Oracle Java plugin can be used in Firefox at the moment and that is the only alternative I have found so far.