  A search for inelastic scattering of Weakly Interacting Massive Particles
(WIMPs) on the isotope $^{129}$Xe was done in data taken with the single phase
liquid xenon detector XMASS at the Kamioka Observatory. Using a restricted
volume containing 41 kg of LXe at the very center of our detector we observed
no significant excess of events in 165.9 days of data. Our background reduction
allowed us to derive our limits without explicitly subtracting the remaining
events which are compatible with background expectations and derive for e.g. a
50 GeV WIMP an upper limit for its inelastic cross section on $^{129}$Xe nuclei
of 3.2 pb at the 90% confidence level.
