  The scalar potential of the MSSM may have local and global minima
characterized by non-zero expectation values of charged and colored bosons.
Even if the true vacuum is not color and charge conserving, the early Universe
is likely to occupy the minimum of the potential in which only the neutral
Higgs fields have non-zero vev's. The stability of this false vacuum with
respect to quantum tunneling imposes important constraints on the values of the
MSSM parameters. We analyze these constraints using some novel methods for
calculating the false vacuum decay rate. Some regions of the MSSM parameter
space are ruled out because the lifetime of the corresponding physically
acceptable false vacuum is small in comparison to the present age of the
Universe. However, there is a significant fraction of the parameter space that
is consistent with the hypothesis that the Universe rests in the false vacuum
that is stable on a cosmological time scale.
