  Results are presented for the first measurement of the double-polarization
helicity asymmetry E for the $\eta$ photoproduction reaction $\gamma p
\rightarrow \eta p$. Data were obtained using the FROzen Spin Target (FROST)
with the CLAS spectrometer in Hall B at Jefferson Lab, covering a range of
center-of-mass energy W from threshold to 2.15 GeV and a large range in
center-of-mass polar angle. As an initial application of these data, the
results have been incorporated into the J\"ulich model to examine the case for
the existence of a narrow $N^*$ resonance between 1.66 and 1.70 GeV. The
addition of these data to the world database results in marked changes in the
predictions for the E observable using that model. Further comparison with
several theoretical approaches indicates these data will significantly enhance
our understanding of nucleon resonances.
