The low-frequency stability of a long thin annular layer of energetic ions in a background plasma with finite axial and zero azimuthal magnetic field is studied analytically. It is found that although the equilibrium is susceptible to the kink instability, low mode number perturbations can be stabilized in the limit of N(i)/N(b) --> O when the current layer is close to the maximum field-reversal parameter. A brief discussion of the tearing mode stability criteria of such strong current layers with respect to the placement of conducting walls is also presented.