As you said YouTube is working fine in all other web browsers but the problem is only with Chrome, then here is the fully working solution for the same.
Open Windows Explorer and go to C:UsersUserNameAppDataLocalGoogleChromeUser DataPepperFlash
Open PepperFlash folder and you will see a folder named as "11.5.31.138"
Simply right click this folder and go to its Properties.
Click "Security" tab, select your username and click Edit.
Check "Allow" for all of the permissions. Click OK.