  First measurement of the beam asymmetry $\Sigma$ for Compton scattering off
the proton in the energy range $E_{\gamma}=0.85 - 1.25$ GeV is presented. The
data reveals two narrow structures at $E_{\gamma}= 1.036$ and
$E_{\gamma}=1.119$ GeV. They may signal narrow resonances with masses near
$1.68$ and $1.72$ GeV, or they may be generated by the sub-threshold $K\Lambda$
and $\omega p$ production. Their decisive identification requires additional
theoretical and experimental efforts.
