When you are faced will a downhill chip shot, the most important thing to consider is that the ball is going to roll, or run, more than it usually would because of the downhill slope that you are facing.
Exactly how much more the shot will run, will depend on the severity of the slope that you are on, but you will definitely experience more run than when playing the chip on a level surface.
To play the most effective chip shot, regardless of slope, always aim to land the ball so that the first bounce it has is on the green, but as close to you as possible. This will allow you to play the easiest shot possible, as landing the ball closest to you will always give you the best result. Once you have identified your landing area, look at how much of the shot is from the ball to the landing area and needs to be in the air and how much is from the landing area to the pin so needs to roll. This will now allow you to select the correct club to play the shot with.
Generally, on a flat surface, if there is a quarter of the shot to the landing area and three quarters of the shot remaining to the flag, you will need to play a 7 iron. If it is half of the shot to the landing area and half of the shot to the flag, you need to play your 9 iron. Finally, if you have three quarters of the shot to the landing area and only a quarter of the shot remaining to the flag, then play your sand iron.
Decide on the club to play the shot with the formula above. Then remember you are now playing a downhill chip so you will get more run. Therefore, adjust your club selection so that you play the shot with a more lofted club. If you had decided it was a 7 iron shot, play it with an 8 iron or even a 9 iron depending on the severity of the slope, but still landing the ball only a quarter of the way to the flag.
As for your set up position, play the shot as you would for a standard chip shot. Have a slightly narrower stance with the ball in the middle. Keep your hands ahead of the club head by creating a straight line from your left shoulder, down to your left hand and then down to the club head. When playing from a downhill lie, place more weight on your lower foot to allow your spine to become perpendicular to the slope. The easy way to remember this would be to allow your shoulders to reflect the angle of the slope that you are playing from. Maintain this position as you swing the straight line of your left shoulder, left hand and club head, back and through the shot. This will allow the club head to travel with the angle of the slope, so that it moves up the slope on the backswing and down the slope on the follow through, ensuring you get a crisp connection with the ball.
Play the shot from a position where your shoulders reflect the angle of the slope that you are on and use a more lofted club than usual, to allow for the extra run that the downhill slope will produce. These tips will get you chipping much more consistently and accurately when playing downhill shots.