Originally posted by Dave Leonard
As swjohnsey mentioned elsewhere, putting a smaller sprocket on the front can cause problems. I'm not all that certain about the ZX-6 layout here, but on the ZX-9, for example, the chain already rides over the swingarm guide making it difficult to achieve the proper chain slack. On these bikes, having an even smaller front sprocket just makes the problem that much worse. You can get the slack just right with the bike on the side stand, but with the rider on board, the chain slack disappears completely. The results in many bikes having their chains set way too tight. This condition also causes the plastic or rubber guide to wear completely through and having the chain start cutting into the swingarm itself. So you might want to consider going up on the rear, as this tends to lift the chain just that much further away from the swingarm. One tooth on the front is about equal to three teeth on the rear, which may be too much reduction, so you'll also have a little more option with the rear.
With that said, is a new chain needed if I were to go up 3 in the back? If so. how much is a new chain.