Originally Posted by
dave.king1
Use thicker strings ;) :D
It was only a guess, but it you are using the plastic nut that could be the issue, if it is only while the string is open then it is almost certainly at that end of the neck.
Put a finger on the string at the back of the nut to hold it still and see if the problem remains, if it goes then the nut is the culprit or the string tree isn't in place and there isn't enough break angle on the string at the headstock and the vibrations are between the nut and the tuner.