We find that if two superconducting islands of different number parity
are linked by a tunnel junction, the unpaired electron in the odd isl
and has a tendency to tunnel into the even island. This process leads
to fluctuations in time of the number parity of each island, giving ri
se to a random telegraph noise spectrum with a characteristic frequenc
y that has an unusual temperature dependence. This new phenomenon shou
ld be observable in a Cooper-pair pump and similar single-electron tun
neling devices.