Hi There,

The picture you sent is just a caterpillar and shouldn't be causing any substantial issues. I wouldn't spray until you are sure of what the issue is--I have a few ideas. Some locations had high numbers of scale and tent caterpillar in the maple stands--if your trees are in proximity to a maple stand from which "honey dew" (scale frass) or tree sap from tent caterpillar feeding could drift this may be what you are seeing.  

Chestnut can also support scale--read more here http://msue.anr.msu.edu/news/lecanium_scale_numbers_building_on_chestnuts 

If you don't see any insects active on the trees there is no reason to treat. You can also check out this page for more possible causes of chestnut issues http://www.canr.msu.edu/chestnuts/pest_management/


Best,
Erin