Charged Higgs production in association with a top quark at approximate NNLO

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.