Many cyclic processes such as neuron firing, cardiac functions, and cell division can exhibit integer variations of their period. Period doubling is often triggered by external events, and is an important phenomenon because it can control a change in the time scale of downstream processes. The capacity for period doubling is also relevant in synthetic molecular circuits where slow and fast modules need to be synchronized. In this paper we describe a rationally designed biomolecular reaction network which operates frequency division of its periodic inputs. The core of this device is a bistable circuit, which is toggled between its two stable states by “push” chemical reactions that process the periodic inputs. We thoroughly analyze the behavior of the system deriving an upper bound on the baseline of the inputs it can process, maintaining its output specifications. All the reactions in the system have first or second order rates, and are potentially implementable in vitro using nucleic acids and enzymes. Numerical analysis shows that frequency division is achieved in a range of realistic parameters.