A new method of formulating dyadic Green's functions in lossless , reciprocal and unbounded chiral medium was presented. Based on Helmholtz theorem and the nondivergence and irrotational splitting of dyadic Dirac delta-function was this method, the electrical vector dyadic Green's function equation was first decomposed into the nondivergence electrical vector dyadic Green's function equation and irrotational electrical vector dyadic Green's function equation, and then Fourier's transformation was used to derive the expressions of the non-divergence and irrotational component of the spectral domain electrical dyadic Green's function in chiral media. It can avoid having to use the wavefield decomposition method and dyadic Green's function eigenfunction expansion technique that this method is used to derive the dyadic Green's functions in chiral media.