We investigate a chain of capacitively coupled Josephson junctions in
the regime where the charging energy dominates over the Josephson coup
ling, exploiting the analogy between this system and a multidimensiona
l crystal. We find that the current-voltage characteristic of the curr
ent-driven chain has a staircase shape, beginning with an (insulating)
nonzero voltage plateau at small currents. This behavior differs qual
itatively from that of a single junction, which should show Bloch osci
llations with vanishing dc voltage. The simplest system where this eff
ect can be observed consists of three grains connected by two junction
s. The theory explains the results of recent experiments on Josephson
junction arrays.