  We create and study persistent currents in a toroidal two-component Bose gas,
consisting of $^{87}$Rb atoms in two different spin states. For a large
spin-population imbalance we observe supercurrents persisting for over two
minutes. However we find that the supercurrent is unstable for spin
polarisation below a well defined critical value. We also investigate the role
of phase coherence between the two spin components and show that only the
magnitude of the spin-polarisation vector, rather than its orientation in spin
space, is relevant for supercurrent stability.
