We report the results of a search for a spontaneous magnetization in t
he superconducting B-phase of UPt3 which is predicted to exist because
of broken time-reversal symmetry. We have measured the change of magn
etic flux upon the superconducting transition in a field very close to
zero by using a SQUID magnetometer. Our result gives the upper limit
of 2 mG for the spontaneous internal held, one order of magnitude smal
ler than obtained by a recent mu SR measurement. The small value favor
s the theory of orbital degeneracy of the pair wave function over the
theory of spin degeneracy.