The Dirac equation in Kerr spacetime is separated using the rotating tetrad formalism. This allows solutions of the Dirac equation, in flat spacetime, written in oblate and prolate spheroidal coordinates to be extracted. The usual MIT bag boundary condition, -i gamma ^mun_v Psi = Psi is then found to be incompatible with a non-vanishing separated wavefunction except in the spherical limit. However, it is shown that an alternative boundary condition exists that is physically motivated and allows for a non-trivial solution.