Unfortunately, there is no hook that runs after creating new categories, which is a shame. (You can find a list of available extension hooks here.)
You could try writing an extension that uses the sessions_end hook, then checks for the various
$_GET variables that indicate that you just created a new category, but that wouldn't account for times when someone submits the "new category" form and receives errors, nor for when someone creates a new category via the links found on the Publish Form (which are created via AJAX).
So your only alternative I believe is to write a module which does this directly by polling the database (looking at
exp_categories) and comparing it to your MailChimp categories, then making changes as required. You would configure this using an "action" (which allows you to trigger your method with a URL like
http://mysite.com/?ACT=10), and setup a cron job on your server to run this acton periodically.
Hope that helps.