An approximate analytic solution of the magnetohydrodynamic (MHD) equilibrium equation for large‐aspect‐ratio, helically symmetric systems is obtained. The resistive ballooning stability of these equilibria is studied numerically and analytically. We find that the ballooning modes scale as the resistivity to the third power. They are driven by the helical nature of the magnetic axis and by the elliptic distortion of the flux surfaces away from a circle.