All you need is the MailChimp for Shopify App installed + configured, then whenever someone fills out the form below, they're added as a new customer to Shopify and for whatever reason the MailChimp integration apparently also sees that a someone who also has opted to receive marketing emails...
{% form 'customer' %}
{{ form.errors | default_errors }}
<input type="email" placeholder="Email Address" name="contact[email]" id="email-input">
<input type="submit" class="button" value="Join" name="subscribe" id="email-submit">
{% endform %}