Records relating to construction of Army airfields during World War II would be in Record Group 18
(Records of the Army Air Forces).
The records are at Archives II. Here is one entry which might contain records you seek:
Contact firstname.lastname@example.org for textual records,
and email@example.com for maps, drawings, and aerial photographs of the airfield.
Chester had an airfield? I was poking around looking and read Spartenburg airport was used for training by the army air forces but didn't see anything much closer than that. Sometimes you can find good records when they closed the base, a friend had luck finding diagrams of a hanger that was built at one of those airfields not around long in property dispoal files can't recall where but it was federal records.
thanks,the airfield was just that not really a base just 3 runways ,1 small
building,no planes ever station there now a county airport.