  We report the results of $^{77}$Se--nuclear magnetic resonance (NMR) in
$\alpha$-FeSe, which exhibits a similar crystal structure to the
LaFeAsO$_{1-x}$F$_x$ superconductor and shows superconductivity at 8 K. The
nuclear-spin lattice relaxation rate $1/T_1$ shows $T^3$ behavior below the
superconducting transition temperature $T_c$ without a coherence peak. The
$T_1T=$ const. behavior, indicative of the Fermi liquid state, can be seen in a
wide temperature range above $T_c$. The superconductivity in $\alpha$-FeSe is
also an unconventional one as well as LaFeAsO$_{1-x}$F$_x$ and related
materials. The FeAs layer is not essential for the occurrence of the
unconventional superconductivity.
