  The quark-connected part of the hadronic light-by-light scattering
contribution to the muon's anomalous magnetic moment is computed using lattice
QCD with chiral fermions. We report several significant algorithmic
improvements and demonstrate their effectiveness through specific calculations
which show a reduction in statistical errors by more than an order of
magnitude. The most realistic of these calculations is performed with a
near-physical, $171$ MeV pion mass on a $(4.6\;\mathrm{fm})^3$ spatial volume
using the $32^3\times 64$ Iwasaki+DSDR gauge ensemble of the RBC/UKQCD
Collaboration.
