To enable integration with the MailChimp, go to Account Management / Integration with other services / Mailout services:
In the list click the checkbox in the MailChimp block:
On the next step you will need to confirm turn on the integration by logging into your MailChimp account.
After that, in each contact filter, you will be able to enable the automatic export of selected contacts to MailChimp (see the Help).
Important: Contacts in MailChimp account updates within a few minutes (usually 7-8). Keep this in mind when planning your mailings.