Grammatical models which represent the hierarchical structure of chord sequences have proven very useful in recent analyses of Jazz harmony. A critical resource for building and evaluating such models is a ground-truth database of syntax trees that encode hierarchical analyses of chord sequences. In this paper, we introduce the Jazz Harmony Treebank (JHT), a dataset of hierarchical analyses of complete Jazz standards. The analyses were created and checked by experts, based on lead sheets from the open iRealPro collection. The JHT is publicly available in JavaScript Object Notation (JSON), a human-understandable and machine-readable format for structured data. We additionally discuss statistical properties of the corpus and present a simple open-source web application for the graphical creation and editing of trees which was developed during the creation of the dataset.