The linear stability analysis of planar detonation waves was studied under a chain branching reaction model. Such kinetics mimics the characteristics and reaction dynamics of hydrogen chemistry, and thus is the motivation of this study. The reaction model is applied to the steady one dimensional Zel'dovich, von-Neumann and Doering (ZND) detonation wave. It consists sequentially of a chain-initiation and chain-branching step both governed by Arrhenius rates, and followed by a temperature-independent chain-termination step where heat release is associated with. The stability analysis involves applying small perturbations to the reference ZND solution and observing for positive growth rates. The initiation activation energy was used as the varying parameter. The stability of the wave is mainly associated with the chain-branching reaction zone. The most challenging factor however, was formulating the downstream boundary condition and applying it far enough downstream where chemistry is more complete. The solution obtained is numerical, as it depends on results from the reference solution, which are only available numerically. Results shows a dominant, unstable mode that becomes non-oscillatory as initiation activation energy increases. Such behavior is consistent with predicted detonation cell mechanisms in literature.