  We present a theory of the anomalous Hall effect in a topological Weyl
superconductor with broken time reversal symmetry. Specifically, we consider a
ferromagnetic Weyl metal with two Weyl nodes of opposite chirality near the
Fermi energy. In the presence of inversion symmetry, such a metal experiences a
weak-coupling Bardeen-Cooper-Schrieffer (BCS) instability, with pairing of
parity-related eigenstates. Due to the nonzero topological charge, carried by
the Weyl nodes, such a superconductor is necessarily topologically nontrivial,
with Majorana surface states coexisting with the Fermi arcs of the normal Weyl
metal. We demonstrate that, surprisingly, the anomalous Hall conductivity of
such a superconducting Weyl metal coincides with that of a nonsuperconducting
one, under certain conditions, in spite of the nonconservation of charge in a
superconductor. We relate this to the existence of an extra (nearly) conserved
quantity in a Weyl metal, the chiral charge.
