  We present results of a search for a neutral, six-quark, dibaryon state
called the \h, a state predicted to exist in several theoretical models.
Observation of such a state would signal the discovery of a new form of
hadronic matter. Analyzing data collected by experiment E799-II, using the KTeV
detector at Fermilab, we searched for the decay $H^0 \to \Lambda p \piminus$
and found no candidate events. We exclude the region of lightly bound mass
states just below the $\Lambda\Lambda$ mass threshold, $2.194~\gev < M_H <
2.231$~\gev, with lifetimes from $\sim$$ 5 \times 10^{-10}$~sec to $\sim$$1
\times 10^{-3}$~sec.
