Just figured this out tonight so I’m still testing; hope it helps:
1) Install the extension Blank Canvas (this allows you to run Grease Monkey Scripts in Chrome): https://chrome.google.com/extensions/detail/pipnnjjknlabchljabhmnpdfpdobpnkk
Note you might have to restart Chrome.
2) Install the Auto BCC script from userscripts: http://userscripts.org/scripts/show/2255
Make sure it installs into Blank Canvas and NOT as a native Chrome extension.
3) Refresh Gmail, create a new message, input a “To” address and then a pop-up will ask you where to auto BCC all new messages. Input your dropbox address.
Now whenever you create a new message or reply/forward, your dropbox will be put in the BCC box. Small bug: you must click the “reply” button in the upper right, not the one at the bottom, or it won’t put in the BCC.
Optionally you can edit the script and add “var gBccPopup = true” which should prompt you each time to ask whether you want to BCC the dropbox. Or you can just delete the address out of the BCC field manually if most of your emails go to the dropbox.
