The closest metro station to Casa de Chiles is Chapultepec. To get to the station turn left leaving the building, and then turn again left in Río Elba. Arriving to Reforma cross to the other side and take the cap on Estrella de Luz, the Bicentenary monument:

Walk with the park and Estrella on the right hand side and head towards a stand of busses. The metro station is just behind: