The molecular dynamics of a chiral liquid crystal showing a rich variety of frustrated mesophases has been investigated by means of 1H NMR relaxometry. The interest in this lactate derivative, HZL 7/*, is related to a large range of thermal stabilities of the twist grain boundary (TGB) phases. Dispersions of the 1H spin-lattice relaxation times, T1, in the frequency range from 300 MHz to 5 kHz were measured and consistently analyzed in the isotropic, chiral nematic, TGBA*, and two TGBC* phases. In the isotropic and N* phases, a three-exponential magnetization decay was observed and assigned to three specific molecular groups of the HZL 7/* (molecular core, methyl, and methylene groups). In the TGB phases, all T1 components merge into a single one. The analysis of the T1 dispersion in the TGBA* phase shows that the translational self-diffusion relaxation mechanism dominates over a broad frequency range and that layer undulations are less relevant than the relaxation contribution associated with the diffusion process across the TGB structure. In the TGBC1* phase, the T1 dispersion presents a strong contribution of in-layer tilt direction fluctuations (T1(-1) proportional to ν(-1/2)), while, in the TGBC2* phase, the linear frequency dependence of T1 could be associated with a much stronger contribution of layer undulations than for the other TGB phases. This is at present the first molecular dynamics investigation on several TGB phases by means of 1H NMR relaxometry.