We analyze the charge-parity (CP) asymmetry in the charged Higgs boson decays to chargino-neutralino pairs, H-+/- -> chi(+/-)(i)chi(0)(j), i = 1, 2, j = 1,...,4. We show first that these modes have a large branching ratio for m(H)(+/-) greater than or similar to 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-+/- -> chi(+/-)(1)chi(0)(2).