In this report we consider the Debye model along with Maxwell's equations (Maxwell-Debye) to model electromagnetic wave propagation in dispersive media that exhibit orientational polarization. We construct and analyze a sequential operator splitting method for the discretization of the Maxwell-Debye system. Energy analysis indicates that the operator splitting scheme is unconditionally stable. We also conduct a truncation error analysis to show that the scheme is rst order accurate in time and second order accurate in space. We compare the operator splitting method to the Yee scheme for discretizing the Maxwell-Debye system via stability, dispersion, and dissipation analyses. Numerical simulations validate the unconditional stability of the scheme.