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(LBL)/(mu)(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(LBL)/(mu)(had) is overestimated. Interpolating, this suggests quoting an upper bound. We obtain a(LBL)/(mu)(had)<1.59x10;{-9} (95% C.L.).