A common feature of many cognitive architectures is a central executive control with a 50-millisecond cycle time. This system determines which action to perform next, based on the current context. We present the first model of this system using spiking neurons. Given the constraints of well-established neural time constants, a cycle time of 46.6 milliseconds emerges from our model. This assumes that the neurotransmitter used is GABA (with GABA-A receptors), the primary neurotransmitter for the basal ganglia, where this cognitive module is generally believed to be located.