You can use mailchimp with the silent send feature.
I even added a useful feature in version 4.0.24 to make a newsletter signup checkbox possible.
4.0.24
(10 Aug 2014)
Added Silent Conditional Field and value settings for the silent send feature on the Advanced tab. Use this optional setting to conditionally disable silent sending unless this field tag and value are selected and submitted. Example usage: Your form has a checkbox to “signup for our newsletter” with the tag “signup-newsletter”. You do a silent send to MailChimp to sign up people to the newsletter but you want to disable the silent send if the checkbox is left unchecked. For this example you will set the Silent Conditional Field to “signup-newsletter” and the Silent Conditional Value to “selected”, this will only match the field tag and value when the checkbox is selected on the form.
Note: I do not use mailchimp, but here are the Silent Sent settings I have seen other people use:
Add a checkbox field to your form “Signup to our newsletter”
set the field name to signup-newsletter
Go to the Advance tab of the form settings:
Silent Remote Sending Settings
Set Silent Remote sending to Enabled Method POST
Enter the URL of your Mailchimp Signup URL
https://kb.mailchimp.com/lists/signup-forms/host-your-own-signup-forms
the url looks formatted like this
(but with your actual yourlisturl and both value information for the u and id
https://yourlisturl/subscribe/post?u=value&id=value
Silent send fields to rename:
first-name=FNAME
last-name=LNAME
email-address=EMAIL
Silent send key value pairs to add:
subscribe=Subscribe
Silent Conditional Field (optional): signup-newsletter
Silent Conditional Value (optional): selected
You should test it a couple times
You may also want to add some field to ignore settings
Silent send fields to ignore:
subject
full_message
akismet
date_time
ip_address
If this does not work, make sure your mailchimp URL is correct and that the url includes the proper u and id values