  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 M\"uller ansatz we conclude ballistic spin transport in SrCuO2.
