  In a program to formulate and develop two-dimensional conformal field theory
in the framework of algebraic geometry, Beilinson and Drinfeld have recently
given a notion of ``chiral algebra'' in terms of D-modules on algebraic curves.
This definition consists of a ``skew-symmetry'' relation and a ``Jacobi
identity'' relation in a categorical setting. In this paper, we show directly
that these chiral algebras are essentially the same as vertex algebras without
vacuum vector (and without grading), by establishing an equivalence between the
skew-symmetry and Jacobi identity relations of Beilinson-Drinfeld and the
(similarly-named, but different) skew-symmetry and Jacobi identity relations in
the formal-variable approach to vertex operator algebra theory as formulated by
Borcherds, Frenkel-Lepowsky-Meurman and Frenkel-Huang-Lepowsky.
