Agree that vacuuming is the key. Be sure your vacuuming does not spread the chalk. USe a TM with Dust downer or HEPA filtered vacuum to avoid spreading the chalk dust back out into the room through the vacuum filter bag.
Use a soft brush along with the vacuuming to loosen as much chalk as possible.
Clean using a filtration soil remover (Filter Free) if it is a spot; Use Traffic Slam. Both contain ingredients to break the bond between very fine soil (chalk dust) and the fiber.
Rinse on the acid side.
If any color remains, try a dye remover such as RedZONE or Red Releif.
Scott Warrington
Technical Support
Interlink Supply / Bridgepoint Systems