We present the first measurement of associated direct photon + muon
production in hadronic collisions, from a sample of 1.8 TeV ppbar collisions
recorded with the Collider Detector at Fermilab.  Quantum chromodynamics (QCD)
predicts that these events are primarily from the Compton scattering process
cg -> c gamma, with the final state charm quark producing a muon.  Hence this
measurement is sensitive to the charm quark content of the proton.  The
measured cross section of 29 +/- 9 pb-1 is compared to a leading-order QCD
parton shower model as well as a next-to-leading-order QCD calculation.