A deuterium NMR (DNMR) study of the TGBA* (twist grain boundary smectic A*) phase in an NMR magnetic field of 9.4 T for the chiral compound 4-[4-(1-methyl heptyloxy)] biphenyl 4-(10-undecenyloxy) benzoate (11EB1M7) is reported. The deuterium two-dimensional (2D) exchange spectra were observed for the first time in this phase. The present study allows us to learn how the helicoidal structures arrange in an external magnetic field. To derive quantitative kinetic parameters of this novel phase, both 1D and 2D experimental spectra were simulated by means of a jump diffusion model. By comparing the experimental and simulated spectra, an accurate determination of the dynamic parameters in the TGBA* phase was obtained. Furthermore, the twist angle between two neighboring smectic A blocks is found as 26 +/- 10 degrees, which is consistent with the X-ray results for similar chiral liquid crystals. The diffusion constant (D-parallel to) is estimated to be 3.2 x 10(-12) m(2)/s at 379.5 K.