Tiger Woods short game improved tremendously when he added more clubs to his chipping options. He's had particular success with a 4-iron on those long chips where you just want to land the ball on the green or in this case the extremely fast fairways at St. Andrews and let it roll out. He used that shot a few times in the British Open at Hoylake (2006) to get the ball on the ground quickly on those tricky greens.
If you'll notice here, Tiger uses his putting grip (a reverse overlap) because it helps keep his hands working together. You'll probably also notice Tiger is not wearing his glove! Everything else is fundamental to good chipping. He sets most of his weight on his left foot and positions the ball back of center in a narrow but slightly open stance. That helps him make a descending blow into the back of the ball. But before you do anything, read the break and pick a spot just over the fringe, or in this case the fairway, where you want to land the ball.
Just like on a putt, try to keep your head still long after impact. That will help you hit the ball solidly and start it on line...
Ultimately, the secret to a great short-game is self-discovery. Developing a full-fledged short game is a must for any golfer, but how you do and learn the skills it is up to you... so hit that practice green!