The current injected into a semiconducting thin film is space-charge limite
d when the total number of electrons crossing per transit time is on the or
der of CV/e. With nanoscale fabrication techniques it is possible, however,
to make the capacitance so small that CV/e is on the order of 1. In this p
aper we determine the properties of space-charge limited current in such a
single-electron regime for a model of a molecular semiconductor for which c
harge transport takes place by hopping. We discuss the similarities with Co
ulomb blockade effects for a linear array of tunnel junctions between metal
islands.