  We compute the inclusive and differential cross sections for the associated
production of a top quark along with a charged Higgs boson at hadron colliders
to next-to-leading order (NLO) in perturbative quantum chromodynamics (QCD) and
in supersymmetric QCD. For small Higgs boson masses we include top quark pair
production diagrams with subsequent top quark decay into a bottom quark and a
charged Higgs boson. We compare the NLO differential cross sections obtained in
the bottom parton picture with those for the gluon-initiated production process
and find good agreement. The effects of supersymmetric loop contributions are
explored. Only the corrections to the Yukawa coupling are sizable in the
potential discovery region at the CERN Large Hadron Collider (LHC). All
expressions and numerical results are fully differential, permitting selections
on the momenta of both the top quark and the charged Higgs boson.
