This can be a very delicate topic. Chips can be very durable, but at the same time be very delicate. In fact, many chippers choose not to clean their chips at all. Some like to retain the "history" of the chip that comes with it, while others are reluctant to clean them for fear of ruining its finish.
If you choose to clean your chips, I recommend a mild dishwashing soap and a soft-bristle toothbrush. The soap is mild enough not to destroy the finish and the soft bristle are gentle enough not to mar the surface - generally.
If you're dealing with an old chip, or one with a delicate inlay or not stamp, you may be better off not cleaning the chip at all. I have partially rubbed-off a hot stamp on an older chip before I realized it had happened. If in doubt about the durability of the chip - I recommend not cleaning it at all.
On the other hand, if you're dealing with a relatively new and durable chip that has some especially stubborn grime, I sometimes spray a more powerful cleaner like 409 or Clorox Cleanup onto the chip and let it sit for a minute or two and then scrub it with a brush (yes, I can hear you more conservative collectors screaming now). This usually works wonders. HOWEVER, you have to be careful about the chips you do this to. Out of 150+ chips, I have had one or two who's colors appeared faded after this process. I do not recommend this method for very valuable or delicate chips.
Also, there are some cleaners on the market made especially for cleaning casino chips. However, since I haven't tried these, I'm unable to comment on their effectiveness.
Finally, the CC>CC has a very good page containing much more information on cleaning chips. visit their chip cleaning page to learn more.
Contributed By: Al Whiting