Thanks - I've just now released an update (Dropzone 2.8) that adds preliminary support for 10.9 (Mavericks).
If you are running the non-Mac App Store version, you can click on the Updates tab in the Dropzone Preferences and then click the Check Now button to upgrade.
If on the Mac App Store version - you can download the update from http://aptonic.com/dropzone/latest
Email me if you need a license for the non-Mac App Store version. Dropzone 2.8 will be released on the Mac App Store shortly.
I'd love to hear if this new version works well under Mavericks for you or any others who are running it