  The discovery of a superconducting phase in sulfur hydride under high
pressure with a critical temperature above 200 K has provided a new impetus to
the search for even higher $T_c$. Theory predicted and experiment confirmed
that the phase involved is H$_3$S with Im-3m crystal structure. The observation
of a sharp drop in resistance to zero at $T_c$, its downward shift with
magnetic field and a Meissner effect confirm superconductivity but the
mechanism involved remains to be determined. Here, we provide a first optical
spectroscopy study of this new superconductor. Experimental results for the
optical reflectivity of H$_3$S, under high pressure of 150 GPa, for several
temperatures and over the range 60 to 600 meV of photon energies, are compared
with theoretical calculations based on Eliashberg theory using DFT results for
the electron-phonon spectral density $\alpha^2$F($\Omega$). Two significant
features stand out: some remarkably strong infrared active phonons at $\approx$
160 meV and a band with a depressed reflectance in the superconducting state in
the region from 450 meV to 600 meV. In this energy range, as predicted by
theory, H$_3$S is found to become a better reflector with increasing
temperature. This temperature evolution is traced to superconductivity
originating from the electron-phonon interaction. The shape, magnitude, and
energy dependence of this band at 150 K agrees with our calculations. This
provides strong evidence of a conventional mechanism. However, the unusually
strong optical phonon suggests a contribution of electronic degrees of freedom.
