  A search for the process $e^+e^- \to \eta^\prime$ has been performed with the
SND detector at the VEPP-2000 $e^+e^-$ collider. The data were accumulated at
the center-of-mass energy of $957.78\pm 0.06$ MeV with an integrated luminosity
of about 2.9 pb$^{-1}$. For reconstruction of the $\eta^\prime$ meson five
decay chains have been used: $\eta^{\prime}\to\eta\pi^+\pi^-$ followed by the
$\eta$ decays to $\gamma\gamma$ and $3\pi^0 $, and $\eta^{\prime} \to
\eta\pi^0\pi^0$ followed by the $\eta$ decays to $\pi^+\pi^-\pi^0$,
$\gamma\gamma$, and $3\pi^0$. As a result, the upper limit has been set on the
$\eta^\prime$ electronic width: $\Gamma_{\eta^{\prime}\to e^+e^-} < 0.0020$ eV
at the 90\% confidence level.
