We show by means of ab initio calculations that the organic molecular crystal TTF-CA is multiferroic: it has an instability to develop spontaneously both ferroelectric and magnetic ordering. Ferroelectricity is driven by a Peierls transition of the TTF-CA in its ionic state. Subsequent antiferromagnetic ordering strongly enhances the opposing electronic contribution to the polarization. It is so large that it switches the direction of the total ferroelectric moment. Within an extended Hubbard model, we capture the essence of the electronic interactions in TTF-CA, confirm the presence of a multiferroic groundstate, and clarify how this state develops microscopically.