The Parikh image of a word abstracts from the order of its letters. Parikh’s famous theorem states that the set of Parikh images of a context-free string language forms a semilinear set that can be effectively computed from its grammar. In this paper we study the computation of Parikh images for graph grammars defined by contextual hyperedge replacement (CHR). Our motivation is to generate efficient predictive top-down (PTD) parsers for a subclass of CHR grammars. We illustrate this by describing the subtask that identifies the nodes of the input graph that parsing starts with.