Please back up all data.
Quit FaceTime if it’s running. Force quit if necessary. After each of the following steps, restart the computer and test. If the problem isn't resolved, quit again and go on to the next step.
Step 1
If you synchronize Contacts with a network service such as iCloud or Google, disable that synchronization in the iCloud or Internet Accounts pane of System Preferences. When prompted to confirm, choose to delete the contacts from the Mac. They'll still be on the servers and on your other devices. Leave the preference pane open.
If FaceTime works now, re-enable Contacts synchronization, wait for the network contacts to reappear, and see what happens.
Step 2
Make sure you know the ID and password you use with FaceTime.
Launch the Keychain Access application in any of the following ways:
☞ Enter the first few letters of its name into a Spotlight search. Select it in the results (it should be at the top.)
☞ In the Finder, select Go ▹ Utilities from the menu bar, or press the key combination shift-command-U. The application is in the folder that opens.
☞ Open LaunchPad and start typing the name.
Select the login keychain from the list on the left side of the Keychain Access window. If your default keychain has a different name, select that.
If the lock icon in the top left corner of the window shows that the keychain is locked, click to unlock it. You'll be prompted for the keychain password, which is the same as your login password, unless you've changed it.
From the menu bar, select
Keychain Access ▹ Keychain First Aid
from the menu bar and repair the keychain.
From the Category list in the lower left corner of the window, select
My Certificates
Look carefully at the list of certificates in the right side of the window. If any of them is marked with a red "X" as expired or invalid, delete it.
Now select
Keychain Access ▹ Preferences... ▹ Certificates
There are three menus in the window. Change the selection in the top two to Best attempt, and in the bottom one to CRL.
Next, select
Passwords
in the Category list. Enter "ids" (without the quotes) in the search box in the toolbar of the window. Delete all items of type "application password" that have a name beginning in any of the following ways:
ids:
IDS:
com.apple.ids:
Also find and delete all items with "facetime" or "com.apple.idms" in the name.
Quit Keychain Access.
Step 3
Hold down the option key and select
Go ▹ Library
from the Finder menu bar. Move the following items from the Library folder to the Trash (some may not exist):
Application Support/CallHistoryDB
Caches/com.apple.imfoundation.IMRemoteURLConnectionAgent
Containers/com.apple.AddressBook.FaceTimeService
Containers/com.apple.corerecents.recentsd
Containers/com.apple.FaceTime
Containers/com.apple.soagent
IdentityServices
Leave the Library folder open.
Step 4
In the Preferences subfolder, there may be several files having names that begin with one of the following strings:
com.apple.facetime
com.apple.FaceTime
com.apple.ids
com.apple.imagent
com.apple.imservice
Move them all to the Trash.
Also in the Preferences folder, there is a subfolder named "ByHost". Open it and do the same thing.