We investigate the merits of a measurement of the permanent electric dipole moment of the electron ( e EDM) with barium monofluoride molecules, thereby searching for phenomena of CP violation beyond those incorporated in the standard model (SM) of particle physics. Although the BaF molecule has a smaller enhancement factor in terms of the effective electric field than other molecules used in current studies (YbF, ThO and ThF + ), we show that a competitive measurement is possible by combining Stark-deceleration, laser-cooling and an intense primary cold source of BaF molecules. With the long coherent interaction times obtainable in a cold beam of BaF, a sensitivity of 5 × 10 −30 e⋅cm for an e EDM is feasible. We describe the rationale, the challenges and the experimental methods envisioned to achieve this target. Graphical abstract