Chess in Madrid that costs nothing 7
Chess groups 2
Clubs 2
Giant boards 1
Open-air boards 1
Tournaments 1
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Free here means the sources state that taking part costs nothing. That covers the Chamartín park sessions on Fridays and Saturdays, the Friday get-together at Academia de Ajedrez Chamberí with the Madrid Chess Meetup, and the Friday club evening of Octava Casilla in Hortaleza, none of which asks for membership.
Two tournaments are free as well: the Vicálvaro district's tournament for non-federated children and young players, which needs registration, and the campus tournaments of Universidad Carlos III, open to its own community only. Ajedrez en el Parque has organised a chess afternoon with free entry and prior sign-up. A free session is not a free club: classes, membership and the same club's tournaments carry their own prices, and those are on the card when published.