The present work investigates the parametric instability of parallel propagating circularly polarized Alfvén (pump) waves in a weakly ionized molecular cloud. It is shown that the relative drift between the plasma particles gives rise to the Hall effect, resulting in the modified pump wave characteristics. Although the linearized fluid equations with periodic coefficients are difficult to solve analytically, it is shown that a linear transformation can remove the periodic dependence. The resulting linearized equations with constant coefficients are used to derive an algebraic dispersion relation. The growth rate of the parametric instability is a sensitive function to the amplitude of the pump wave as well as to the ratio of the pump and the modified dust-cyclotron frequencies. The instability is insensitive to the plasma β. The results are applied to the molecular clouds.