The massless fermions of a Weyl semimetal come in two species of opposite chirality, in two cones of the band structure. As a consequence, the current j induced in one Weyl cone by a magnetic field B [the chiral magnetic effect (CME)] is canceled in equilibrium by an opposite current in the other cone. Here, we show that superconductivity offers a way to avoid this cancellation, by means of a flux bias that gaps out a Weyl cone jointly with its particle-hole conjugate. The remaining gapless Weyl cone and its particle-hole conjugate represent a single fermionic species, with renormalized charge e∗ and a single chirality ± set by the sign of the flux bias. As a consequence, the CME is no longer canceled in equilibrium but appears as a supercurrent response ∂j/∂B=±(e∗e/h2)μ along the magnetic field at chemical potential μ.