This paper describes a scheme for implementing a binary counter with chemical reactions. The value of the counter is encoded by logical values of 0 and 1 that correspond to the absence and presence of specific molecular types, respectively. It is incremented when molecules of a trigger type are injected. Synchronization is achieved with reactions that produce a sustained three-phase oscillation. This oscillation plays a role analogous to a clock signal in digital electronics. Quantities are transferred between molecular types in different phases of the oscillation. Unlike all previous schemes for chemical computation, this scheme is dependent only on coarse rate categories for the reactions (fast and slow). Given such categories, the computation is exact and independent of the specific reaction rates. Although conceptual for the time being, the methodology has potential applications in domains of synthetic biology such as biochemical sensing and drug delivery. We are exploring DNA-based computation via strand displacement as a possible experimental chassis.