Toponym matching, i.e. pairing strings that represent the same real-world location, is a fundamental problemfor several practical applications. The current state-of-the-art relies on string similarity metrics, either specifically developed for matching place names or integrated within methods that combine multiple metrics. However, these methods all rely on common sub-strings in order to establish similarity, and they do not effectively capture the character replacements involved in toponym changes due to transliterations or to changes in language and culture over time. In this article, we present a novel matching approach, leveraging a deep neural network to classify pairs of toponyms as either matching or nonmatching. The proposed network architecture uses recurrent nodes to build representations from the sequences of bytes that correspond to the strings that are to be matched. These representations are then combined and passed to feed-forward nodes, finally leading to a classification decision. We present the results of a wide-ranging evaluation on the performance of the proposed method, using a large dataset collected from the GeoNames gazetteer. These results show that the proposed method can significantly outperform individual similarity metrics from previous studies, as well as previous methods based on supervised machine learning for combining multiple metrics.