Hi Brian. I have been a member of CardsChat for over six months, and this is the first chip question that I have seen (and I've been looking). I have cleaned thousands if not tens of thousands of chips. To give an accurate and safe answer to this question, I need to know what kind of chips you are trying to clean. A picture would help. But the short answer is that liquid dish washing detergent is safe for all chip types that I am aware of. A quick soak and a light scrub with a plastic scrubbing surface (like you use for teflon) or toothbrush will handle all but the toughest gunge.
If your chips have inlays (the "paper" looking "stickers" in the middle of the chips) it may be necessary to limit soak time. This depends on the type of chips you have. Some are much more sensitive than others.
War is Peace, Freedom is Slavery, Ignorance is Strength - and here you thought this was so "37 Years Ago"
We played for many times with the poker chips I have and actually never thought of cleaning them. They do start to look a little dirty but if I wash them it will be ruined again after one game (chips, pizza, fried stuff,... no chance).