This error is caused due to a problem with the cache folder that battle.net created on your computer.
To fix this open the “C:\ProgramData\Blizzard Entertainment\Battle.net” folder on Vista or Win 7. Windows XP users can find this at “C:\Documents and Settings\All Users\Application Data\Blizzard Entertainment\Battle.net”.
You should see a folder called “Cache”. Rename this folder to any other name or delete it. Now start Diablo 3 and the error should be fixed.
I did this first, then I was getting another Error.
Error 315300. So I did an old fix that I have done with this in the past.
Create a NEW user account on your Windows machine (make it an administrator). Login to this Windows account, run Diablo and you should be able to login to Diablo without any issues! :) (maybe the odd Error 37 though)