  We present experiments on the thermal transport in the spin-1/2 chain
compound copper pyrazine dinitrate Cu(C_4 H_4 N_2)(NO_3)_2. The heat
conductivity shows a surprisingly strong dependence on the applied magnetic
field B, characterized at low temperatures by two main features. The first one
appearing at low B is a characteristic dip located at mu_B B ~ k_B T, that may
arise from Umklapp scattering. The second one is a plateau-like feature in the
quantum critical regime, mu_B |B-B_c| < k_B T, where B_c is the saturation
field at T=0. The latter feature clearly points towards a momentum and field
independent mean free path of the spin excitations, contrary to theoretical
expectations.
