Mailchimp Sync Plugin

First, it is still in beta, so it is something to be aware.
Also, it mentions synchronizing with from WP to MC and S2M does that already.

If you want a powerful bidirectional synchronisation between s2M and MC, check this video: https://www.youtube.com/watch?v=YMQPejazwqg See if this is what you need.
And there is a free version also, which has only a few features but might be enough for what you need if you only want the emails to synchronise.