We investigated the relative influence of cellular and network properties on the extreme spike timing precision observed in the medullary pacemaker nucleus (Pn) of the weakly electric fish Apteronotus leptorhynchus. Of all known biological rhythms, the electric organ discharge of this and related species is the most temporally precise, with a coefficient of variation (CV = standard deviation/mean period) of 2 × 10−4 and standard deviation (SD) of 0.12–1.0 μs. The timing of the electric organ discharge is commanded by neurons of the Pn, individual cells of which we show in an in vitro preparation to have only a slightly lesser degree of precision. Among the 100–150 Pn neurons, dye injection into a pacemaker cell resulted in dye coupling in one to five other pacemaker cells and one to three relay cells, consistent with previous results. Relay cell fills, however, showed profuse dendrites and contacts never seen before: relay cell dendrites dye-coupled to one to seven pacemaker and one to seven relay cells. Moderate (0.1–10 nA) intracellular current injection had no effect on a neuron's spiking period, and only slightly modulated its spike amplitude, but could reset the spike phase. In contrast, massive hyperpolarizing current injections (15–25 nA) could force the cell to skip spikes. The relative timing of subthreshold and full spikes suggested that at least some pacemaker cells are likely to be intrinsic oscillators. The relative amplitudes of the subthreshold and full spikes gave a lower bound to the gap junctional coupling coefficient of 0.01–0.08. Three drugs, called gap junction blockers for their mode of action in other preparations, caused immediate and substantial reduction in frequency, altered the phase lag between pairs of neurons, and later caused the spike amplitude to drop, without altering the spike timing precision. Thus we conclude that the high precision of the normal Pn rhythm does not require maximal gap junction conductances between neurons that have ordinary cellular precision. Rather, the spiking precision can be explained as an intrinsic cellular property while the gap junctions act to frequency- and phase-lock the network oscillations.