Existing approaches for Chinese zero pronoun resolution typically utilize only syntactical and lexical features while ignoring semantic information. The fundamental reason is that zero pronouns have no descriptive information, which brings difficulty in explicitly capturing their semantic similarities with antecedents. Meanwhile, representing zero pronouns is challenging since they are merely gaps that convey no actual content. In this paper, we address this issue by building a deep memory network that is capable of encoding zero pronouns into vector representations with information obtained from their contexts and potential antecedents. Consequently, our resolver takes advantage of semantic information by using these continuous distributed representations. Experiments on the OntoNotes 5.0 dataset show that the proposed memory network could substantially outperform the state-of-the-art systems in various experimental settings.