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We formulate a linear response theory of the chiral magnetic effect in afinite Weyl semimetal, expressing the electrical current density $j$ induced bya slowly oscillating magnetic field $B$ or chiral chemical potential $\mu$ interms of the scattering matrix of Weyl fermions at the Fermi level. Surfaceconduction can be neglected in the infinite-system limit for $\delta j/\delta\mu$, but not for $\delta j/\delta B$: The chirally circulating surface Fermiarcs give a comparable contribution to the bulk Weyl cones no matter how largethe system is, because their smaller number is compensated by an increased fluxsensitivity. The Fermi arc contribution to $\mu^{-1}\delta j/\delta B$ has theuniversal value $(e/h)^2$, protected by chirality against impurity scattering--- unlike the bulk contribution of opposite sign.

Scattering theory of the chiral magnetic effect in a Weyl semimetal: Interplay of bulk Weyl cones and surface Fermi arcs