  We analyze the charge-parity (CP) asymmetry in the charged Higgs boson decays
to chargino-neutralino pairs, H^- -> chargino_i + neutralino_j. We show first
that these modes have a large branching ratio for m_H^- > 600 GeV. We use
Cutkosky rules to obtain the analytical formulas needed for the evaluation of
the asymmetry under consideration. We then calculate the CP asymmetry in
chargino-neutralino decays by including supersymmetric mass bounds, as well as
constraints from b -> s gamma, (g-2)_mu, Delta\rho and electric dipole moments.
Finally, we discuss observability of the asymmetry at the LHC by calculating
the number of required charged Higgs events to observe the asymmetry for each
decay channel. We show that the inclusion of constraints considerably reduces
the projected CP asymmetry, and that the optimal channel for observing the
asymmetry is H^- -> chargino_1 + neutralino_2.
