We investigate a chain of capacitively coupled Josephson junctions in the regime where the charging energy dominates over the Josephson coupling, exploiting the analogy between this system and a multi-dimensional crystal. We find that the current-voltage characteristic of the current-driven chain has a staircase shape, beginning with an (insulating) non-zero voltage plateau at small currents. This behavior differs qualitatively from that of a single junction, which should show Bloch oscillations with vanishing dc voltage. The simplest system where this effect can be observed consists of three grains connected by two junctions. The theory explains the results of recent experiments on Josephson junction arrays.

5 pages, 4 figures included