We report zero and longitudinal magnetic field muon spin relaxation (μSR) measurements of the spin S = 1/2 antiferromagnetic Heisenberg chain material SrCuO2. We find that in a weak applied magnetic field B0 the spin-lattice relaxation rate λ follows a power law λ is proportional to B(0)(-n) with n = 0.9(3). This result is temperature independent for 5 K ≤ T ≤ 300 K. Within conformal field theory and using the Müller ansatz we conclude ballistic spin transport in SrCuO2.