Adding custom CSS classes to individual Widgets

Hello. I’m almost finished with my first WordPress theme but I’ve run into a snag. I’d like allow the admin to set a custom CSS class for each individual Widget from the Widgets admin page.

I’ve actually already created this theme as a Joomla template first, now I’m working on the WordPress theme version. In the Joomla admin panel you can give each Module (Widget) a custom CSS class, which is applied to the div containing the Module.

I’d like to figure out how to make this happen in WordPress as well. Is there any plugin out there that would automatically add an extra field to each widget’s options, or any other way to allow a site admin to designate a text string for individual widgets?

Thanks!