Constituency parsing is an important task of informing how words are combined to form sentences. While constituency parsing in English has seen significant progress in the last few years, tools for constituency parsing in Indonesian remain few and far between. In this work, we publish ICON (Indonesian CONstituency treebank), the hitherto largest publicly available manually-annotated benchmark Indonesian constituency treebank with a size of 10,000 sentences and approximately 124,000 constituents and 182,000 tokens, which can support the training of state-of-the-art transformer-based models. As part of the process of building the treebank, we review and revamp the constituent and POS tagsets in use in existing treebanks to ensure that the labels are relevant and suitable for the grammatical features of Indonesian. We establish strong baselines on the ICON dataset using the Berkeley Neural Parser with transformer-based pre-trained embeddings, with the best performance of 88.85% F1 score coming from our own version of SpanBERT (IndoSpanBERT). We further analyze the predictions made by our best-performing model to reveal certain idiosyncrasies in Indonesian that pose challenges for constituency parsing.