  Let $E$ be an arbitrary graph and $K$ be any field. We construct various
classes of non-isomorphic simple modules over the Leavitt path algebra
$L_{K}(E)$ induced by vertices which are infinite emiters, closed paths which
are exclusive cycles and paths which are infinite, and call these simple
modules Chen modules. It is shown that every primitive ideal of $L_{K}(E)$ can
be realized as the annihilator ideal of some Chen module. Our main result
establishes the equivalence between a graph theoretic condition and various
conditions concerning the structure of simple modules over $L_K(E)$.
