Original:  Parts of the southern Chancay area were conquered by the Chim in the early fifteenth century and in about 1450 A.D. the Incas were occupying both areas.
Revised:  Parts of the southern Chancay area were conquered by the Chim in the early 1400s, and by about 1450 A.D. the Incas were occupying both areas.
Edit intent: clarity