Nuclear magnetic spin relaxation times T1, T2 and Tip have been measured for methyl and acid protons in pivalic acid throughout the plastic crystalline phase, 6"9 to 36"5~ Tip and T2 of the methyl protons are interpreted in terms of translational self-diffusion of molecules. Diffusion coefficients are deduced which are in fair agreement with previous radiotraeer measurements. T1 measurements at 10 MHz and 20"8 MHz indicate molecular reorientation and the temperature dependence of this process is investigated. Tip and T2 measurements for the acid protons show that they move more rapidly through the lattice than the molecules. This is in agreement with previously reported tracer studies. A mechanism is proposed connecting the anomalously fast hydrogen atom diffusion and molecular reorientation, which is consistent with the N.M.R. and tracer measurements.