It is proposed to use TF muSR to study the low temperature, low field part of the phase diagram of Ba3CuSb2O9, a system with a uniform triangular lattice of S=1/2 Cu ions that is believed to provide an example of a triangular lattice quantum spin liquid. Measurements will be made in a similar manner to those recently reported by us in the 31st March 2011 issue of Nature for a molecular dimer based quantum spin liquid system. The dependence of the TF spectrum on temperature, applied fields up to 20 mT and angle of the applied field with respect to the spin lattice planes will be studied in detail, following intriguing data obtained at PSI in 2011, that showed evidence for in-plane spin currents at low temperatures. The frequency resolution, data rate and flexibility of sample environment at ISIS make EMU or HIFI the most suitable instruments for such a follow on investigation.