First of all, you may instruct your users to turn on NPAPI support on the Chrome flags page. It seems to be feasible even for untrained users, see details how to do it. We are preparing a quick fix which will automatically display appropriate instructions for Chrome users.
However it is a temporary relief. In 6 months Google will remove this ability as well. So the only advice is to migrate to the HTML5 uploader if you did not do it yet.
The first link is useful to understand if HTML5 uploader is lacking of some important features you are using in Java uploader. The second one contains some instructions how to migrate.
Don't worry if you find that some of the important features are not in the ready list yet. We are going to add all features mentioned there sooner or later. If some of the features are super-critical, please let us know so that we could prioritize our release plans.
Curious what feature of that list is in progress? At this moment we are working on the image editor functionality and it will be released in the nearest weeks. I will post about it when it is available.