  The elastic properties of a filled skutterudite PrOs_4Sb_{12} with a heavy
Fermion superconductivity at T_C=1.85 K have been investigated. The elastic
softening of (C_{11}-C_{12})/2 and C_{44} with lowering temperature down to T_C
indicates that the quadrupolar fluctuation due to the CEF state plays a role
for the Cooper paring in superconducting phase of PrOs_4Sb_{12}. A Debye-type
dispersion in the elastic constants around 30 K revealed a thermally activated
Gamma_{23} rattling due to the off-center Pr-atom motion obeying
tau=tau_{0}exp(E/k_{B}T) with an attempt time tau_0=8.8*10^{-11} sec and an
activation energy E=168 K. It is remarkable that the charge fluctuation of the
off-center motion with Gamma_{23} symmetry may mix with the quadrupolar
fluctuation and enhance the elastic softening of (C_{11}-C_{12})/2 just above
T_C.
