Here we present some unique observations of reconnection at a quasi‐perpendicular bow shock as an interplanetary directional discontinuity (DD) is crossing it simultaneously with the Magnetospheric Multiscale (MMS) mission. There are no burst data, but available data show indications of ongoing reconnection at the shock southward of MMS: a bifurcated current sheet with signatures of Hall magnetic and electric fields, normal magnetic fields indicating a magnetic connection between the two reconnecting regions, field‐aligned currents and electric fields, E·J>0 indicating a conversion of magnetic to kinetic energy, and subspin resolution ion energy‐time spectrograms indicating ions being accelerated away from the X‐line. The DD is also observed by four upstream spacecraft (ACE, WIND, Geotail, and ARTEMIS P1) and one downstream in the magnetosheath (Cluster 4), but none of them resolve signatures of ongoing reconnection. We therefore suggest that reconnection was temporarily triggered as the DD was compressed by the shock. Reconnection at the bow shock is inevitably asymmetric with both the density and magnetic field strength being higher on one side of the X‐line (magnetosheath side) than on the other side where the plasma flow also is supersonic (solar wind side). This is different from the asymmetry exhibited at the more commonly studied case of asymmetric reconnection at the magnetopause. Asymmetric reconnection of the bow shock type has never been studied before, and the data discussed here present some first indications of the properties of the reconnection region for this type of reconnection.