SharePoint 2013 – User Profile Synchronization Service not starting

While trying to start the User Profile Synchronization Service the status showed as Starting for about a minute then went straight back to Stopped.  The ULS log, filtered by ‘User Profiles’ category, contained the following entries:

SetupFIMBuildSpecificRegistryKeys: Exception trying to
write
‘HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\PowerShell\1\PowerShellSnapIns\MIIS.MA.Config’:
System.UnauthorizedAccessException: Access to the registry key
‘HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\PowerShell\1\PowerShellSnapIns\MIIS.MA.Config’
is denied.

and

ProfileSynchronizationService: Provisioning Timer Job
encountered an exception: System.UnauthorizedAccessException: Access to the
registry key
‘HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\PowerShell\1\PowerShellSnapIns\MIIS.MA.Config’
is denied.

I almost always encounter an issue of some kind when provisioning the User Profile Synchronization Service but this is the first time I’ve seen these errors.  Luckily it didn’t take long to fix as I had identified the service account specified was not a member of the local administrators group, which is a requirement during the provisioning process.