Cesium-133 NMR spectra of a single crystal of Cs2CrO4 (space group Pnma) were obtained as a function of crystal orientation in an applied magnetic field of 4.70 T and analyzed to provide the magnitudes and orientations of the Cs-133 chemical shielding and quadrupolar tensors for each of the two crystallographically distinct Cs sites. These NMR-characterized nuclear sites have been assigned to the crystallographic sites based on the local symmetry and results of a point-charge model of the electric field gradient tensors. The results indicate that the chemical shielding and quadrupolar interactions are not coincident for either distinct Cs-133 nucleus in the crystal lattice. For each site, the principal axis system of the Cs-133 chemical shielding tenser is oriented along the crystallographic a, b, c axes, while the orientation of the electric field gradient tenser deviates from these axes, by 7 degrees and 52 degrees in the crystallographic plane of symmetry. The Cs-133 chemical shielding tensors span spectral widths of the order of 300 ppm, which is comparable to the range of isotropic chemical shifts for this isotope.