Chinchón is within driving distance of Madrid city centre and Madrid airport, reachable within 40-50 minutes.
Arriving from Madrid airport - approx. 40 minute drive, €40-50 by Uber.
If you would like to use public transportation from Madrid city centre, you can get the C3 renfe cercanías train (https://www.redtransporte.com/madrid/cercanias-renfe/linea-c-3.html) until ciempozuelos and then get the bus 416 (https://www.redtransporte.com/madrid/autobuses-interurbanos/416-valdemoro-villaconejos-colmenar-de-oreja.html) until Chinchon.