We report zero and longitudinal magnetic field muon spin relaxation measurements of the spin S=1/2 antiferromagnetic Heisenberg chain material SrCuO2. We find that in a weak applied magnetic field B the spin-lattice relaxation rate follows a power law B^n with n=-0.9(3). This result is temperature independent for 5K < T < 300 K. Within conformal field theory and using the Muller ansatz we conclude ballistic spin transport in SrCuO2.
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