High-precision DC magnetization (M) measurements have been performed on a single crystal of copper pyrazine dinitrate (CuPzN) in magnetic fields H up to 14.7 T at temperatures down to 0.08 K. This material is one of the best realizations of a one-dimensional (1D) S = 1/2 Heisenberg antiferromagnet. At the base temperature, full saturation of M is observed above H s = 13.97 T with the M(H) curve closely following a prediction based on the Bethe ansatz. The peak in M(T ), which appears at about 7 K in zero field, moves to lower temperatures with increasing H and vanishes into a temperature region well below 0.08 K at H ∼ H s ; as a result, M(T ) exhibits a strong upturn as T → 0 at this field, in agreement with a theoretical prediction. These results constitute an observation of field-induced quantum critical behavior in bulk magnetization.