This paper considers the behavior of a master-slave system of two coupled piecewise constant spiking oscillators (PWCSOs). The master of this system exhibits chaos and outputs a chaotic sequence of spikes, which are used as input to the slave. The slave exhibits a periodic-like trajectory (PLT) that is chaotic but that appears to be periodic in the phase plane. We theoretically investigate the generating region of the PLT in the parameter space. Using a test circuit, we confirm the typical phenomena of this coupled system.