Its not currently possible to do automatically. You can automate the extraction of new clients fairly easily using Scheduled Reports. The output can be emailed or written to a file for later import to MailChimp.

I'm not familiar with MailChimp, but it looks like its just a matter of adding new contacts to a list?

If so, it could be done with a plugin which would be configured with:

• the list identifier i.e. the MailChimp list the contacts are added to
• the report to run, to extract the contact data
• how frequently the load runs (e.g. daily, weekly)

There would need to be a flag added to customers to enable them to opt-out of marketing emails.