Cobalt-59 NMR spectra of a single crystal of tris(2,4-pentanedionato-O,O’) cobalt(III) were obtained as a function of crystal orientation in an applied magnetic field of 9.40 T. The analysis provides the magnitudes and orientations of the Co-59 nuclear quadrupole coupling and chemical shift tensors for each of the two magnetically distinct but crystallographically equivalent cobalt sites. The cobalt electric field gradient and chemical shift tensors are not coincident, but their unique components are close to the approximate C-3 axis of the complex. Small deviations from perfect octahedral symmetry at the cobalt nucleus result in a significant nuclear electric field gradient and highly anisotropic chemical shift. The cobalt nuclear quadrupolar coupling constant is 5.53 +/- 0.10 MHz with an asymmetry of 0.219 +/- 0.005, while the chemical shift tensor has a span of 1174 +/- 25 ppm. The principal components relative to the isotropic chemical shift, delta(iso) = 12498 +/- 5 ppm, are delta(11) = 698 +/- 22 ppm, delta(22) = -222 +/- 12 ppm, and delta(33) = -476 +/- 5 ppm. The quadrupolar tensor was characterized by examining splittings between the satellite transitions, while the chemical shift tensor was characterized by analyzing the central transition and correcting for the second-order quadrupolar interaction. The results obtained in this study are compared with those of previous Co-59 NMR studies.