While your first course of action should be to take steps to prevent your chips from getting dirty in the first place, with care, poker chips can be cleaned. However, with a set containing hundreds of chips, it can be a very slow and tedious process.
Plastic and plastic composite chips, provided they have no imprinting, label or decal, can be easily cleaned by gentle rubbing with a damp cloth. Clumps of dirt can be removed with gentle scraping with a soft object (eg. the edge of another chip), but never with anything hard, like metal, that could gouge or scratch the chip or with anything abrasive. Indentations can be cleaned by gentle brushing with a soft bristle toothbrush. While they can be immersed for a short period in cool water, do not allow them to soak. Do not immerse or rinse with hot water. Dry with a soft cloth.
Clean the surface of your table before the game.
Wash your hands before playing and after eating.
Keep food and drinks off the table and wipe up spills as quickly as possible.
Avoid serving finger foods.
Avoid serving oily or greasy foods.
There is wide variability in the composition of poker chips, so before embarking on a cleaning, test your procedure completely from beginning to end on just one chip to make sure it does not harm the chip. These suggestions are not intended for use on collectable gaming chips.