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Using new and archival radio data, we have measured the proper motion of the black hole X‐ray binary V404 Cyg to be  9.2 ± 0.3 mas yr −1  . Combined with the systemic radial velocity from the literature, we derive the full three‐dimensional heliocentric space velocity of the system, which we use to calculate a peculiar velocity in the range 47–102 km s −1 , with a best‐fitting value of 64 km s −1 . We consider possible explanations for the observed peculiar velocity and find that the black hole cannot have formed via direct collapse. A natal supernova is required, in which either significant mass  (∼11 M ⊙ )  was lost, giving rise to a symmetric Blaauw kick of up to ∼65 km s −1 , or, more probably, asymmetries in the supernova led to an additional kick out of the orbital plane of the binary system. In the case of a purely symmetric kick, the black hole must have been formed with a mass  ∼9 M ⊙  , since when it has accreted  0.5–1.5 M ⊙   from its companion.

The formation of the black hole in the X‐ray binary system V404 Cyg