The magnetic susceptibility and single-crystal X-ray structure of the one-dimensional Heisenberg antiferromagnetic chain tetramethylammonium manganese trichloride (TMMC) have been studied under pressure as a facile route to develop structure-property relationships. The X-ray structure of TMMC was determined at 0, 2.1, 3.8, 6.8, 12.2, and 17.0 kbar using diamond-anvil cell techniques and synchrotron radiation. The space group is confirmed to be P6(3)/m up to 17 kbar, and structural refinement shows that the Mn-Mn separations between and along the chains change by about 3.4 and 2.5%, respectively, over 17 kbar. A structural transition from hexagonal to monoclinic symmetry possibly occurs at 17 kbar, associated with a loss of crystal quality. Variable-temperature magnetic susceptibility data were taken at 0, 0.3, 1.5, 2.9, 4.0, 5.2, and 6.5 kbar and show that the intrachain coupling constant changes from -6.85 to -7.81 K over this range. The interchain coupling constant of -0.54 K can also be extracted from the Fisher model modified for interacting chains. The pressure-temperature diagram shows the slope of the intrachain antiferromagnetic coupling with pressure, DeltaT(IAF)/DeltaP, changes from 0.5 to 1.6 K/kbar at 2 kbar where the structure changes from P2(1)/a to P2(1)/m. Comparison of the magnetic and structural data are consistent with the power-law relationship developed by Bloch where J proportional, variant r-n, r = Mn...Mn separation and n approximately 10.