UPDATE: As of September 1st, 2015 Google released Chrome version 45 which completely blocks all NPAPI plugins including the Unity Web Player. Users will need to use either Internet Explorer, Firefox, Safari, or Opera to run the Unity Web Player. We are hard at work developing a replacement application that will remove the need for the Unity Web Player however there is currently no time frame for its release.
The Chrome browser no longer support the Unity Web Player plugin. If you try to install the plugin you may find yourself in an endless loop of installations. The quickest way to get the application running is to switch to one of the other support browsers: Internet Explorer, Firefox, Safari, & Opera. It is no longer possible to use the Unity Web Player in Chrome.