How to Fix Messages
The following steps worked for me:
Update December 2016 - this happened once more - this fixed it again, so I'm even more certain of it now.
Clear PRAM (NVRAM)
Hold Cmd ⌘+Opt ⌥+P+R at the chimes until they are heard for a second time, then release
Start in Safe Mode
As soon as you hear the second chimes hold Shift ⇧ & keep holding until you see the regular startup progress thermometer
Attempt to login to iMessage.
Mine at this point appeared to fail & the iMessage login screen just went grey.
I stared at it for 5 minutes, then rebooted.
Recommended but Unsuccessful
These things were recommended elsewhere but they did not work for me:
- Checking Firewall settings til I was blue in the face.
It worked yesterday & still works for all other machines in the house...
- Changing DNS provider.
- Logging out of everything iCloud related then back in again.
- Any amount of messing with the keychain - Repairing, Erasing
- Restoring random items in
~/Library/Preferences; including, at one point, the entire folder
- 'Repair install' using latest Combo Update.
- Recovering entire drive from a day-old known-good clone.
- Reinstalling entire OS from Time Machine.
I'm copying this answer to all relevant Stack Exchange questions, in case it helps others. You would not believe the amount of chasing round I did to fix this one ;-)
 Many articles (& Keychain Repair itself) claim that
com.apple.security.plist ought to be owned by the user - in fact every time you fix that, next reboot it reverts to being owned by
I gave up trying to 'cure' that as it appeared to make no difference in the end.