This is an older thread but I found a solution that I wanted to share.
1. Sign up for a free gmail account at
www.gmail.com
2. After logging in to your gmail account, click settings at the top, click the Forwarding and POP/IMAP "tab", and make sure that IMAP is enabled (it should be by default).
3. Open Thunderbird and set up an IMAP account to gmail using the instructions at
Thunderbird 2.0 - Help Center.
4. You can now drag your Thunderbird data and drop it into your gmail account from within the Thunderbird GUI. You can actually drag and drop entire folders!
5. After you've moved all of your data to Thunderbird, set up your gmail account in zimbra and synch it. Your data has now been migrated.