Orbital viscosity is usually associated with the A phase of superfluid 3He which has a finite orbital angular momentum even in zero magnetic field. The B phase has no orbital angular momentum in zero magnetic field, but both spin and orbital angular momenta are induced by a field. The Leggett equations for spin dynamics assume that the orbital angular momentum can only charge on timescales much longer than those involved in spin dynamics. We calculate the orbital viscosity of the B phase in both the hydrodynamic and ballistic limits. At low temperatures the orbital viscosity becomes vanishingly small which gives rise to the possibility of coupled spin-orbit dynamics.