In-situ high pressure viscosity measurements, using synchrotron X-ray radiography, have been carried out on liquid Fe-S (8.5 wt.% S) at pressures up to 6 GPa and at 1823 K. Here we show that (i) the effect of pressure on the isothermal viscosity is substantial, with an apparent activation volume of 5.8 cm3/mol; and (ii) viscosity is constant along the pressure dependent melting boundary. Assuming the independence of viscosity along the melting boundary up to core pressures, our results yield a viscosity for the Earth's outer core, at the inner core boundary, of 1.6 ¿ 10-2 Pa s. On this basis, we present a revised viscosity profile across the outer core.