  We report $^{121,123}$Sb NQR studies on single crystals of the narrow gap
semiconductor Ce3Au3Sb4. The temperature dependence of the nuclear quadrupole
frequency ($\nu_Q$), as well as the magnetic susceptibility, is well explained
by crystal electric field effects. The nuclear spin-lattice relaxation rate
($T_1^{-1}$) of both $^{121}$Sb and $^{123}$Sb increases rapidly with
decreasing temperature. The ratio of $T_1^{-1}$ for the two Sb isotopes is
constant at high temperature but it decreases at low temperatures, indicating
the important role of quadrupole fluctuations of the Ce ions. We propose that
quadrupole fluctuations could be the origin of the large specific heat at low
temperature via phonon-quadrupole moment coupling.
