The linear stability of the Bénard layer with the combined effects of a uniform magnetic field and a uniform angular velocity in the presence of a Hall current is examined using the Boussinesq approximation. Assuming the directions of the magnetic field and angular velocity to be both vertical, for time-independent motions the problem is studied for different types of boundaries using an asymptotic analysis for large Taylor and Hartmann numbersTandMrespectively. The Hall current is found to have a significant influence on the onset of convection. When the Hall constant,m, is of order unity the critical Rayleigh number (R) is found to increase withmwhenTlies in the range O(M4) ≤T≤ O(M6) for all types of boundaries. For largem, that is whenm= O(Ms), (s> O) for free insulating boundaries the Hall current is found to affectRwhenT≤ O(M3). In the case of free perfectly conducting boundaries, whenm= O(M) andT≤ O(M2), the Hall current is found to influenceRto leading order.