We study the Josephson current through a superconducting grain coupled
by two tunnel junctions to macroscopic superconducting leads. As a re
sult of the Coulomb blockade we predict the critical Josephson current
to have a threshold behavior when the superconducting gap is suppress
ed below the charging energy by a magnetic field. This effect is a dir
ect consequence of a discrimination by the superconducting ground stat
e between odd and even number of electrons on the grain. The critical
current is periodically modulated by the voltage of a gate electrostat
ically coupled to the grain. We find a characteristic change in this m
odulation at the threshold.