Shots that are on or around the green do not require power, they require touch. Therefore, the golfer should grip the club very lightly for putts and chips because increased grip pressure decreases feel and inhibits a natural swinging motion. The golfer should have the sense that they are gripping the club lightly enough to actually 'feel' the clubhead contact the ball.
Remember that grip pressure should remain consistent for the entire stroke. Many beginners and high handicappers have a tendency to grip the club with more pressure as it approaches the ball on the downswing in an effort to control the shot. Trying to control or manipulate the club in this fashion is an 'anti-touch' move, resulting in many fat, thin, and muffed shots around the green, and poor distance control while putting.
I do recommend that the golfer grip the club with a bit more pressure in the left hand than the right (for right-hand golfers). The left hand is the 'control' hand and the right hand is the 'power' hand, so it thereby makes sense to add control and decrease power. Another danger in gripping too hard with the right hand is the dreaded 'flip' shot in which the right hand unhinges through impact, breaking down and flipping (or 'scooping') the club at the ball rather than lagging it through. This is the number one reason for failed chip and pitch shots around the green, because the club does not stay square through impact for nearly as long as a lagging motion that is achieved by keeping the wrists firm through contact.
A good way to get a sense of how much grip pressure should be used for putts and chips is to hold the club so that she shaft is vertical with the clubhead in the air. Hold the club just firmly enough so that it does not slip out of your hands (about a five on a scale from one to ten). Then, increase the grip pressure in the left hand just slightly. Try to maintain this same pressure as you address your ball and throughout the entire stroke.
Think of feeling the weight of the clubhead throughout the stroke. If you ever lose the feel for where the clubhead is, then you are gripping too tight. Get out of your own way and let the club swing back and through rather than trying to guide or manipulate it.
