1. Go to admin/config/services/mailchimp/lists/1/edit
2. Check ONLY the "authenticated user" at the Roles section and Save
3. Go back to admin/config/services/mailchimp/lists/1/edit
4. Check "Enable MailChimp webhooks for this list" at the Settings section and Save
5. Seems everything ok, but when you go back the setting, the "Enable MailChimp webhooks for this list" checkbox is unchecked.
6. Check again, and after Save the error says "Unable to connect webhooks: Setting up multiple WebHooks for one URL is not allowed."
7. If you uncheck the authenticated user (and of course check another custom role), Save, go back, check the "Enable MailChimp webhooks for this list" and Save again, it will work.
At least for me :)

Comments

These lines comes to the log in the meantime:

  1. Notice: Undefined index: data in mailchimp_process_webhook() (line 334 of /web/www/sites/all/modules/mailchimp/mailchimp.module).
  2. Notice: Undefined index: type in mailchimp_process_webhook() (line 335 of /web/www/sites/all/modules/mailchimp/mailchimp.module).
  3. Notice: Undefined index: type in mailchimp_process_webhook() (line 351 of /web/www/sites/all/modules/mailchimp/mailchimp.module).
  4. Webhook type has been processed.

Playing more with the "Enable MailChimp webhooks for this list" feature, I've found that if you set the checkbox succesfully and edit the list again the checkbox will be an "uncheckbox". Just save it again and again.
(with Optional and Required list also the same error)

Another related thread:
#1706014: List Is Not Syncing

Status:Active» Closed (cannot reproduce)

Error is your post from the web hooks is coming back empty, although I have no way of knowing why. Cannot recreate.