I just started using the Mailchimp List Subscribe Form plugin (to replace an older plugin that no longer is supported) and immediately had the same problem. I installed the WP Armour Honeypot plugin. It works well with WordPress sign-ins and the regular contact form, and has a list of other forms it can also work with, but unfortunately the Mailchimp form isn’t one of them. I’ve contacted the developers and they’ve added it to their to-do list, but in the meantime I’m looking for some other way to secure the form. I thought about using Akismet, but it’s a bit pricey for my tastes and it’s not clear to me that it covers the WordPress form. (Still have to check on that.) Any other suggestions would be welcome.