The question of whether the spin transport in an S=1/2 Heisenberg antiferromagnetic chain is ballistic or diffusive remains intensely discussed theoretically and studied experimentally. While spin transport in an integrable spin-1/2 chain would normally be expected to be ballistic, a number of experiments have found evidence for either type of transport of different systems and even cross-over regimes in certain systems. These findings can be explained in the context of recent theoretical work by Sirker et al. [1] who argue that both channels are present, with a cross-over taking place at an energy scale determined by the magnetic exchange and temperature. Here we propose to study the spin transport in the highly-ideal spin-1/2 chain SrCuO2, which due to its very large exchange constant (J=2100 K) should allow sensitive tuning between the two competing regimes in large magnetic fields.