  The composition of gamma-ray burst (GRB) ejecta is still a mystery. The
standard model invokes an initially hot ``fireball'' composed of baryonic
matter. Here we analyze the broad band spectra of GRB 080916C detected by the
Fermi satellite. The featureless Band-spectrum of all five epochs as well as
the detections of >~10 GeV photons in this burst place a strong constraint on
the prompt emission radius, which is typically >~ 10^{15} cm, independent on
the details of the emission process. The lack of detection of a thermal
component as predicted by the baryonic models strongly suggests that a
significant fraction of the outflow energy is initially not in the ``fireball''
form, but is likely in a Poynting flux entrained with the baryonic matter. The
ratio between the Poynting and baryonic fluxes is at least ~(15-20) at the
photosphere radius, if the Poynting flux is not directly converted to kinetic
energy below the photosphere.
