We propose to measure the asymmetry for polarized photoproduction of charmed quarks from polarized targets in End Station A at SLAC, using a large solid angle muon spectrometer. A quasi-monochromatic circularly po larized photon beam will be produced from an oriented diamond crystal. The targets will be longitudinally polarized LiD and NHs at a temperature of 0.4 K, centered in a 7 T magnetic field to obtain high polarization. Photoproduction of open charm will be tagged by decays of D mesons into high transverse momentum muons. The L/R asymmetry for producing open charm is closely related to the fundamental polarized gluon spin density AG(z). The asymmetry for single muons will be measured as a function of muon momentum, muon transverse momentum, and photon beam energies with sufficient precision to discriminate among models of AG(z) that differ from each other by as little as 10% in the range 0.1 < z < 0.5. Significant constraints will be placed on both the shape and magnitude of AG(z) in this z region. The projected errors are significantly smaller than for other experiments that plan to make direct measurements of AG(z). We request four months of data taking at 120 Hz (assuming joint running with PEP II), and one month of checkout time to carry out this proposal.