This tip is from FastChimpy
First of all, make sure the App is completley closed (Force Quit). Then open Spotlight Search and copy the "~/Library/..." term from down below to get fastest access to your library. Or open Finder and click on "Go to" on the very top of your screen and select "Go to Folder..." and then copy the "~/Library/..." term from down below.
Messages:
1. Navigate to ~/Library/Messages/ and delete all files in this folder.
2. Navigate to ~/Library/Preferences/ and delete the file "com.apple.iChat.plist".
FaceTime:
1. Navigate to ~/Library/Application Support/FaceTime/ and delete all files in this folder.
2. Navigate to ~/Library/Preferences/ and delete the file "com.apple.FaceTime.plist".
Afterwards, simply restart your device and you should be fine.