The Web Development Blog has a tutorial posted showing how to add a Mailchimp "subscribe" feature to your current contact forms. They make use of the MailChimp API wrapper library to make the calls back to the service and subscribe the user at their request.

MailChimp is a great email marketing service provider with an easy to use control panel and features like: campaign management (RSS-driven, A/B Split, Plain-text and regular), statistics, auto-responder and a complete set of list management tools. They offer different ways to place a subscriber form on your website or blog. If you to like add the MailChimp subscribe feature to your existing contact form you need to add some custom code.

They start with a few things you'll need to do to prepare for the connection including the setup of an API key to make the request. He provides a simple "Contact Us" form for reference and the code needed on submit to validate the input and make the subscription call to the API with the email the user provided. He also includes a bit of response handling.