  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 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 $5\times10^{-30}$ e$\cdot$cm for an $e$EDM is feasible. We describe the
rationale, the challenges and the experimental methods envisioned to achieve
this target.
