A set of four electromagnetic dyadic Green's functions of a spherical cavit
y filled with a chiral medium are rigorously derived. The orthogonality of
the eigenmodes of the cavity are employed to allow the use of the method of
scattering superposition in the derivation. This greatly simplifies the de
rivation procedure. The resonant frequencies for the lossless case are obta
ined from the dyadic Green's functions and agree exactly with published res
ults. The derived dyadic Green's functions can be used to formulate integra
l equations for the cavity and are important tools for obtaining numerical
solutions of the cavity by the moment method.