Tina Mickelson offers her advice on chipping from a greenside rough in this video golf lesson. It is important for golfers to note that they will not be able to get the same backspin on the ball in a greenside rough that they would on a tighter lie, which means that the ball needs a higher trajectory.
In order to get the ball higher, the stance and the clubface need to be fairly open, and then during the swing, accelerate through the ball. When finishing, be sure that the club is pointed in the same direction as your target line. Even though the rough prevents the golf ball from getting any backspin, the added height will get the ball to the green.