One-dimensional quantum statistics has been studied at the limit of isotropic exchange interaction in the unpaired electron system of a ferromagnetic organic radical crystal, 3-(4-chlorophenyl)-1,5-diphenyl-6-oxoverdazyl. The characteristic field dependence of the magnetic heat capacity of this crystal is quantitatively explained by the theoretical values derived from the Bethe-ansatz technique applied to the quantum transfer matrix, with a unique intrachain exchange constant J/k(B)=5.5 K. By the simultaneous measurement of magnetic susceptibility and heat capacity, the three-dimensional ordering at T-c=0.21 K, which is triggered by a weak interchain coupling \zJ'\/k(B)=3 x 10(-2) K, is confirmed.