The problem of a steady boundary layer or sheath between a plasma and a magnetic field is considered. A self-consistent transition layer is found which joins a uniform magnetic field at plus infinity with a collisionless field-free plasma region with arbitrary velocity distribution at minus infinity; i.e., a magnetic field profile is found such that the exact particle orbits in this field produce a current which gives rise to the field. An interesting mathematical feature of the ``thinnest'' such solution is that, with any nonsingular velocity distribution at minus infinity, the magnetic field penetrates only a finite distance into the plasma although the plasma extends to infinity, exponentially attenuated, into the magnetic field region. The scale of length is the ratio of the speed of light to the plasma frequency or, equivalently, the Larmor radius of a representative particle. Electric fields arising from charge separation in the case of particles of different mass are ignored.