  We report the results of a search for the inelastic scattering of weakly
interacting massive particles (WIMPs) in the XENON1T dark matter experiment.
Scattering off $^{129}$Xe is the most sensitive probe of inelastic WIMP
interactions, with a signature of a 39.6 keV de-excitation photon detected
simultaneously with the nuclear recoil. Using an exposure of 0.89 tonne-years,
we find no evidence of inelastic WIMP scattering with a significance of more
than 2$\sigma$. A profile-likelihood ratio analysis is used to set upper limits
on the cross-section of WIMP-nucleus interactions. We exclude new parameter
space for WIMPs heavier than 100 GeV/c${}^2$, with the strongest upper limit of
$3.3 \times 10^{-39}$ cm${}^2$ for 130 GeV/c${}^2$ WIMPs at 90\% confidence
level.
