  There are indications that hadronic loops in some electroweak observables are
almost saturated by parton level effects. Taking this as the hypothesis for
this work, we propose a genuine parton level estimate of the hadronic
light-by-light contribution to the anomalous magnetic moment of the muon, a_mu
(LBL,had). Our quark mass definitions and values are motivated in detail, and
the simplicity of our approach allows for a transparent error estimate. For
infinitely heavy quarks our treatment is exact, while for asymptotically small
quark masses a_mu (LBL,had) is overestimated. Interpolating, this suggests
quoting an upper bound. We obtain a_mu (LBL,had) < 1.59 10^-9 (95% CL).
