Exchange 2010 – The user has insufficient access rights when deleting a mailbox

While attempting to remove an old user mailbox from an Exchange 2010 environment (using the EMC) I encountered an access denied error:

Error: Active Directory operation failed on <domain controller>.  this error is not retriable.  Additional information: Access is denied.
Active Directory response: 00000005; SecErr: DSISD-03152763, problem 4003 (INSUFF_ACCESS_RIGHTS), data 0
The user has insufficient access rights

Well, as I’m an Exchange Administrator and haven’t had trouble deleting mailboxes in the past, I assumed this must be a permissions issue in AD itself, so I went looking around the security settings of the object in AD Users and Computers.  Simply granting myself Full Control of the user object was sufficient to resolve this one!