In this paper, an extension of the electric-magnetic current combined-field integral equation (JMCFIE) is presented for the efficient analysis of EM scattering by an arbitrary shaped homogenous chiral object located above a lossy half space. This formulation can lead to a well tested equation system using the method of moments (MoM) solution with the vector triangular basis functions and Galerkin's method. The multilevel fast multipole algorithm (MLFMA) is then employed to reduce the memory requirement and computational complexity of the MoM solution. The inner-outer flexible generalized minimal residual (FGMRES) method is used to further speed up the convergence. The accuracy and efficiency are confirmed with a couple of numerical examples.