The instability of the positive column of an atmospheric argon Poiseuille plasma arc in an axial magnetic field of the order of 100 G was studied both experimentally and theoretically. The instability was manifest as a helical oscillation of the conducting core. The neutral stability curves of frequency versus applied magnetic field for various arc currents and flow rates were obtained by studying the growth or decay of artificially created helical disturbances. The wavelengths of the helix at neutral stability were measured. The critical magnetic fields for the naturally excited oscillation were measured and found to be higher than that at neutral stability. A linearized stability analysis was developed. The theoretical results predict well the frequency and the shape of the neutral stability curves. From both the experiment and the theory, it was found that the destabilizing force is the J × B force and the stabilizing mechanisms are the viscous and the thermal effects.