  A stable neutralino $\chi_1^0$, assumed to be the lightest supersymmetric
particle, is a favored particle physics candidate for the cosmological Dark
Matter. We study co-annihilation of the lightest neutralino with the lighter
scalar top quark $\tilde{t}_1$. We show that for natural values of the
neutralino mass, $\lsim 300$ GeV, the $\chi_1^0 - \tilde{t}_1$ mass difference
has to exceed $\sim 10$ to 30 GeV if $\chi_1^0$, is to contribute significantly
to the Dark Matter. Scenarios with smaller mass splitting, where $\tilde{t}_1$
is quite difficult to detect at collider experiments, are thus cosmologically
disfavored. On the other hand, for small $\tilde{t}_1 - \chi_1^0$ mass
splitting, we show that co--annihilation allows very large neutralino masses,
$m_{\chi_1^0} \sim 5$ TeV, without ``overclosing'' the Universe.
