  Associated selectron-neutralino production in the process $e^-\gamma\to\tilde
e^-\tilde\chi^0$ provides a striking supersymmetric signal: events with a
single high $p_\perp$ electron and otherwise only invisible particles. For
$e^-\gamma$ collisions obtained at high energy linear colliders through
back-scattering of a laser beam, this reaction is shown to be complementary to
selectron pair production in the processes $e^+e^-\to\tilde e^+\tilde e^-$ and
$e^-e^-\to\tilde e^-\tilde e^-$, and to be a probe of heavy selectrons beyond
the kinematical limit of pair production. The standard model background from
$e^-\gamma\to e^-Z^0$ and $W^-\nu$ is studied and substantially reduced by
rapidity and transverse momentum cuts. The minimum required integrated
luminosities for observing this \susic\ signal are given as functions of
several model parameters and collider energies.
