  Discerning the radiative dissipation mechanism for prompt emission in
Gamma-Ray Bursts (GRBs) requires detailed spectroscopic modeling that straddles
the $\nu F_{\nu}$ peak in the 100 keV - 1 MeV range. Historically, empirical
fits such as the popular Band function have been employed with considerable
success in interpreting the observations. While extrapolations of the Band
parameters can provide some physical insight into the emission mechanisms
responsible for GRBs, these inferences do not provide a unique way of
discerning between models. By fitting physical models directly this degeneracy
can be broken, eliminating the need for empirical functions; our analysis here
offers a first step in this direction. One of the oldest, and leading,
theoretical ideas for the production of the prompt signal is the synchrotron
shock model (SSM). Here we explore the applicability of this model to a bright
{\it Fermi} GBM burst with a simple temporal structure, GRB {\it 090820}A. Our
investigation implements, for the first time, thermal and non-thermal
synchrotron emissivities in the RMFIT forward-folding spectral analysis
software often used in GBM burst studies. We find that these synchrotron
emissivities, together with a blackbody shape, provide at least as good a match
with the data as the Band GRB spectral fitting function. This success is
achieved in both time-integrated and time-resolved spectral fits.
