User Profile Synchronization Service stuck on Starting

I am provision the User Profile Service Application in a SharePoint 2013 farm.  Unsurprisingly, it failed to start (it always does for me, for one reason or another).  This time I located the following error in the ULS logs:

ILM Configuration: Error ‘ERR_INVALID_GROUPS’.

This was easy to fix by (temporarily) adding the farm account to the local Administrators group and trying again.  Now the service has started.

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