The MailChimp Integration Add-on Module has been released in beta.  The package can be downloaded from the add-ons page.

It is important to note that this module is only compatible with the new WP-Members 2.8.0 version.  2.8 is presently a beta release, but the current release candidate is pretty close to the final production release.  The reason for this is that the module has some settings tied into the plugin’s options and 2.8 introduces a new admin panel, so it could not be integrated with 2.7.7 and earlier.

If you cannot upgrade WP-Members, you can still integrate using the various hooks in the plugin.