Analytical solutions of electromagnetic fields in the elliptical core chiral optical fiber have been studied. The modal fields distribution and modal characteristic equations are obtained. The numerical solutions for the modal characteristic equations of the even and odd fundamental mode are given. For different aspect ratios of the elliptical core, effects of chirality parameter on the characteristics such as dispersion curves, birefringence and modal dispersion of the fundamental modes in the elliptical core chiral optical fiber are discussed.