  QCD inequalities are derived for the masses of mesons and baryons containing
a single heavy quark using the heavy quark effective field theory. A rigorous
lower bound is obtained for the $\bar\Lambda$ parameters of the heavy quark
effective theory that parameterize $1/m$ corrections, $\bar\Lambda$ > 237 MeV
for mesons, and $\bar \Lambda > 657$ MeV for baryons. The inequalities on
$\bar\Lambda$ imply the inequalities $m_c < 1627$ MeV and $m_b < 5068$ MeV for
the mass parameters of the heavy quark effective field theory.
