If your Contacts List screen has been customized, the MailChimp integration may not be visible.
You can turn it on for the your Contacts grid, but you will need to ensure the following columns are added to the grid:
The columns do not need to be visible, but they do need to exist in the grid.
To enable the Sent to MailChimp option:
MailChimp is now available from the export icon.