  We search for new charmless decays of neutral $b$--hadrons to pairs of
charged hadrons with the upgraded Collider Detector at the Fermilab Tevatron.
Using a data sample corresponding to 1 fb$^{-1}$ of integrated luminosity, we
report the first observation of the \BsKpi decay, with a significance of
$8.2\sigma$, and measure $\BR(\BsKpi) = (5.0 \pm 0.7\stat \pm 0.8\syst)\times
10^{-6}$. We also report the first observation of charmless $b$--baryon decays
in the channels \Lbppi and \LbpK with significances of $6.0\sigma$ and
$11.5\sigma$ respectively, and we measure $\BR(\Lbppi) = (3.5 \pm 0.6\stat \pm
0.9\syst)\times 10^{-6}$ and $\BR(\LbpK) = (5.6 \pm 0.8\stat \pm
1.5\syst)\times 10^{-6}$. No evidence is found for the decays \BdKK and
\Bspipi, and we set an improved upper limit $\BR(\Bspipi) < 1.2\times 10^{-6}$
at the 90% confidence level. All quoted branching fractions are measured using
$\BR(\BdKpi)$ as a reference.
