Alright, well off to LDAP it is.
When you have an alias, this is what Zimbra creates:
In the user account (dn: uid=user,ou=people,dc=domain,dc=com), there are two attributes that are added for the alias:
mail:
alias@domain.com
zimbraMailAlias:
alias@domain.com
Then it also creates another dn for the alias: (dn: uid=alias,ou=people,dc=domain,dc=com with the objectClass of zimbraAlias). In your case, since the alias and the account are the same, that dn is the same.
So you are going to want to delete ONLY the "zimbraMailAlias:
user@domain.com" from the dn for the user.
If you want me to double-check your LDAP before you do this, send me a PM and I will give you my email address for you to send a dump of your LDAP config to make sure that nothing gets hosed up.