If you select “Build for App Store”, the compile errors with the message that a Distribution Profile is required. However, I see no mechanism for specifying my Distribution Profile.
How do we specify our Distribution Profile?
You don’t need to specify it- just make sure it is installed on your local machine. Once you’ve generated a distribution profile on the Apple iOS portal, then you can go to Xcode…Accounts…View Details and hit the reload button in the lower left. You should now see an iOS Distribution signing identity listed up top, and you’ll be good to go.
Like this? 
You have the distribution signing identity, but it does not appear you have a distribution profile installed yet. Are you sure you have a Distribution profile created/listed in your Apple account? See here:
Had similar problem and had to logout of my Xcode account and log back in to get proper refresh.
HTH, Tony
Thanks Tony. That sorted it out. The Distribution profile (with the proper entitlements) is now visible in Xcode and the project builds for the App Store.
I moved my development environment to a new machine while my MacBook is being repaired. I have this problem all over again, and replicated all the steps to get it to build without luck.
Last time I had to wipe all my certificates and profiles before it would work. Not really good.
It would be great if someone could write an app that examined the system and could report if everything needed is there, and if not, specifically what is needed to correct.