  We identify an intrinsic mechanism of the anomalous Hall effect for
non-symmorphic chiral superconductors. This mechanism relies on both a
nontrivial multi-band chiral superconducting order parameter, which is a
mixture of pairings of even and odd angular momentum channels, and a complex
normal state inter-sublattice hopping, both of which are consequences of the
nonsymmorphic group symmetry of the underlying lattice. We apply this mechanism
to the putative chiral superconducting phase of the heavy-fermion
superconductor $\mathrm{UPt_3}$ and calculate the anomalous ac Hall
conductivity in a simplified two-band model. From the ac Hall conductivity and
optical data we estimate the polar Kerr rotation angle and compare it to the
measured results for $\mathrm{UPt_3}$ [E. R. Schemm \textit{et al.}, Science
\textbf{345},190(2014)].
