Discourse analysis is a highly applicable area of natural language processing. In English and other languages, resources for discourse-based tasks are widely available. Thai, however, has hitherto lacked such resources. We present the Thai Discourse Treebank, the first, large Thai corpus annotated in the style of the Penn Discourse Treebank. The resulting corpus has over 10,000 sentences and 18,000 instances of connectives in 33 different relations. We release the corpus alongside our list of 148 potentially polysemous discourse connectives with a total of 340 form-sense pairs and their classification criteria to facilitate future research. We also develop models for connective identification and classification tasks. Our best models achieve an F1 of 0.96 in the identification task and 0.46 on the sense classification task. Our results serve as benchmarks for future models for Thai discourse tasks.