Yes, there is a limit of 3000 contacts per account. TinyLetter is intended for personal use; a simple way to help you stay in contact with your followers or fans. It's not designed for businesses looking to send promotional messages to their customers. If you require greater functionality, it may behoove you to consider exploring other email services that are better suited for business, such as Constant Contact or MailChimp.
If you planned to use TinyLetter as described above, but you're actually pretty popular and have a large contact list, get in touch with our support team.