Graph grammars based on contextual hyperedge replacement (CHR) extend the generative power of the well-known hyperedge replacement (HR) grammars to an extent that makes them useful for practical modeling. Recent work has shown that acyclicity is a key condition for parsing CHR grammars efficiently. In this paper we show that acyclicity of CHR grammars is decidable and that the generative power of acyclic CHR grammars lies strictly between that of HR grammars and unrestricted CHR grammars.