Using an open-flow reactor periodically perturbed with light, we observe sub-harmonic frequency locking of the oscillatory Belousov-Zhabotinsky chemical reaction at one sixth the forcing frequency (6:1) over a region of the parameter space of forcing intensity and forcing frequency where the Farey sequence dictates we should observe one third the forcing frequency (3:1). In this parameter region the spatial pattern also changes from slowly moving traveling waves to standing waves with a smaller wavelength. Numerical simulations of the FitzHugh-Nagumo equations show qualitative agreement to the experimental observations and indicate the oscillations in the experiment are a result of period doubling.