This paper reports 139 La NMR measurements of a powder sample of the colossal magnetoresistance compound La 2/3 Ca 1/3 MnO3 (Tc =268K) performed in the paramagnetic state (292K-575K) and in high magnetic fields (2.00-9.40 Tesla). Analysis of the spectrum measured at 575K establishes that the spectrum is a standard powder pattern broadened to a significant degree by a variation in lattice distortions around lanthanum nuclear sites. At lower temperatures, but still above Tc, the spectrum shifts and broadens. Both the shift and broadening exhibit Curie-Weiss behavior, indicating that the shift measures the polarization of the electron spin system, and the broadening reflects a distribution of magnetic susceptibilities. This distribution may result from variations of local susceptibility in the bulk of the sample or from differences in demagnetizing factors among powder grains. Close inspection of the spectrum indicates that the lattice distortions do not change as the temperature lowers. Spectral diffusion measurements suggest that the temperature dependence of the spectrum shape does not result from freezing out of motion of magnetic polarons. Variations in the nuclear spin-lattice relaxation across the spectrum indicate that magnetic fluctuations, not lattice vibrations, dominate nuclear relaxation. Nuclear spin-lattice relaxation therefore measures electron spin dynamics in this system. The magnetic field dependence of the spin-lattice relaxation indicates that the electron spin-spin correlation function adopts simple single exponential behavior with a slow field-independent correlation time of 10 −8 seconds near Tc. The spin-spin correlation function changes form at higher temperatures and can be described by introducing a field dependence to the correlation time and to the magnitude of the fluctuating field. Even at the highest temperatures, the correlation time remains slow, on the order of 10 −9 seconds. The spin-lattice relaxation therefore indicates the presence of extremely slow dynamics above Tc.