High-field magnetization, field-dependent specific heat measurements, and zero-field inelastic magnetic neutron scattering have been used to explore the magnetic properties of copper pyrazine dinitrate ͓Cu(C 4 H 4 N 2 )(NO 3 ) 2 ͔. The material is an ideal one-dimensional spin-1/2 Heisenberg antiferromagnet with nearest-neighbor exchange constant Jϭ0.90(1) meV and chains extending along the orthorhombic a direction. As opposed to previously studied molecular-based spin-1/2 magnetic systems, copper pyrazine dinitrate remains gapless and paramagnetic for g B H/J at least up to 1.4 and for k B T/J at least down to 0.03. This makes the material an excellent model system for exploring the Tϭ0 critical line that is expected in the H-T phase diagram of the one-dimensional spin-1/2 Heisenberg antiferromagnet. We present accurate measurements of the Sommerfeld constant of the spinon gas versus g B H/JϽ1.4 that reveal a decrease of the average spinon velocity by 32% in that field range. The results are in excellent agreement with numerical calculations based on the Bethe ansatz with no adjustable parameters. ͓S0163-1829͑99͒11201-3͔