  In this paper we introduce an analog of the (classical) Yang-Baxter equation
(CYBE) for vertex operator algebras (VOAs) in its tensor form, called the
vertex operator Yang-Baxter equation (VOYBE). When specialized to level one of
a vertex operator algebra, the VOYBE reduces to the CYBE for Lie algebras. To
give an operator form of the VOYBE, we also introduce the notion of relative
Rota-Baxter operators (RBOs) as the VOA analog of relative RBOs (classically
called $\mathcal{O}$-operators) for Lie algebras. It is shown that
skewsymmetric solutions $r$ to the VOYBE in a VOA $U$ are characterized by the
condition that their corresponding linear maps $T_r:U'\to U$ from the graded
dual $U'$ of $U$ are relative RBOs. On the other hand, strong relative RBOs on
a VOA $V$ associated to an ordinary $V$-module $W$ are characterized by the
condition that their antisymmetrizers are solutions to the $0$-VOYBE in the
semidirect product VOA $V\rtimes W'$. Specializing to the first level of a VOA,
these relations between the solutions of the VOYBE and the relative RBOs for
VOAs recover the classical relations between the solutions of the CYBE and the
relative RBOs for Lie algebras.
