  We present the one-loop QCD amplitudes for two external massless quarks and
three external gluons ($\bar{q}qggg$). This completes the set of one-loop
amplitudes needed for the next-to-leading-order corrections to three-jet
production at hadron colliders. We also discuss how to use group theory and
supersymmetry to minimize the amount of calculation required for the more
general case of one-loop two-quark $n$-gluon amplitudes. We use collinear
limits to provide a stringent check on the amplitudes.
