The lineshape and spin-lattice relaxation times have been measured in solid 1,3,5 cycloheptatriene between 50 K and the melting point. The linewidth change which occurs below the heat capacity transition point of 154 K indicates considerable molecular motion. The very low value for the second moment of the lineshape (0.8 G²) cannot be explained by any simple motion, and various possibilities are discussed. This motion is governed by an activation energy of 6.1+or-0.5 kcal mol^-1. Above the transition point, where the lattice spacing is known, free quasi-isotropic reorientation is occurring, coupled with molecular diffusion at an increasing rate.