  I present approximate next-to-next-to-leading-order (aNNLO) total and
differential cross sections for charged Higgs production in association with a
top quark at LHC energies. The aNNLO results for the process $bg \rightarrow
tH^-$ are derived from next-to-next-to-leading-logarithm (NNLL) resummation of
soft-gluon corrections. Scale and parton-distribution uncertainties for the
cross sections are shown. The top-quark transverse-momentum and rapidity
distributions are also calculated.
