High field mangetization, 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(C4H4N2)(NO3)2). The material is an ideal one-dimensional spin-1/2 Heisenberg antiferromagnet with nearest neighbor exchange constant J=0.90(1) meV and chains extending along the orthorhombic a-direction. As opposed to previosly studied molecular-based spin-1/2 magnetic systems, coppyer pyrazine dinitrate remains gapless and paramagnetic for g mu_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 T=0 critical line which is expected in the H - T phase diagram on the one-dimensional spin-1/2 Heisenberg antiferromagnet. As a first example of such a study we present accurate measurements of the Sommerfeld constant of the spinon gas versus g mu_B H/J < 1.4 which reveal a decrease of the averages 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.