We discuss a theoretical description of the edge current in a chiral superconductor. On the basis of the quasiclassical Green function formalism, we derive a useful expression of the chiral edge current which enable us to understand how Cooper pairs contribute to the electric current. We will show that the chiral edge current is carried by the combinations of two Cooper pairs belonging to different pairing symmetries. One Cooper pair belongs to the usual even-frequency pairing symmetry class. However, the other belongs to the odd-frequency symmetry class.