Using the density-matrix renormalization-group technique we study the
long-wavelength properties of the spin S = 3/2 nearest-neighbor Heisen
berg chain. We obtain an accurate value for the spin velocity upsilon
= 3.87 +/- 0.02, in agreement with experiment. Our results show conclu
sively that the model belongs to the same universality class as the S
= 1/2 Heisenberg chain, with a conformal central charge c = 1 and crit
ical exponent eta = 1.