It should work by removing the permission to comment from the anonymous role.
Thank you, this worked perfectly.
For anyone else reading this, this is how it is done:
1) Go to the Dashboard
2) Under Users click on Roles
3) Either click on Anonymous or click Edit to the right (same result).
4) In the section Orchard.Comments Feature under Permission -
Add comment remove the check mark to the right under Allow.
5) Click Save (bottom of page)