  We derive QCD sum rules for heavy baryons at leading order in $1/m_Q$ and at
next-to-leading order in $\alpha_s$. The calculation involves the evaluation of
four different perturbative three-loop diagrams which determine the
$\alpha_s$-corrections to the Wilson coefficients of the leading term in the
Operator Product Expansion (OPE). From the sum rules we obtain estimates for
the masses and the residues of the heavy baryons $\Lambda_Q$ and $\Sigma_Q$.
The perturbative $O(\alpha_s)$ corrections to the leading order spectral
function amount to about $100%$, and they shift the calculated values for the
baryon masses slightly upward. The residues are shifted upward by about
$20-50%$. For the bound state energy $\bar\Lambda$ given by the difference of
the heavy baryon mass and the pole mass of the heavy quark $m_Q$ we obtain
$m_{\Lambda_Q}-m_Q=780 MeV$ and $m_{\Sigma_Q}-m_Q=950 MeV$. For the residues we
find $|F_\Lambda|=0.028 GeV^3$ and $|F_\Sigma|=0.039 GeV^3$.
