  We study effects of CP violation in an associated production of a charged
Higgs boson and a top quark at the LHC: $pp \to tH^\pm +X$. We calculate the CP
violating asymmetry between the total cross section for $H^+$ and $H^-$
production at next-to-leading order in the MSSM, and perform a detailed
numerical analysis. In the production only the asymmetry is of the order of
20%. The asymmetry in the production and any subsequent decay of an on-shell
charged Higgs boson is to a good approximation the sum of the asymmetry in the
production and the asymmetry in the decay. We consider subsequent decays of
$H^\pm $ to $tb$, $\nu_\tau \tau^\pm$ and $Wh^0$. In the case of subsequent
$H^\pm \to tb$ decay, the $W^\pm - H^\pm$ self energy contributions from the
production and the decay cancel. However, the remaining effect, mainly due to
CP violating box graphs with gluino can go up to $\sim 13$%.
