We explore the task of automatically classifying dialogue acts in 1-on-1 online chat forums, an increasingly popular means of providing customer service. In particular, we investigate the effectiveness of various features and machine learners for this task. While a simple bag-of-words approach provides a solid baseline, we find that adding information from dialogue structure and inter-utterance dependency provides some increase in performance; learners that account for sequential dependencies (CRFs) show the best performance. We report our results from testing using a corpus of chat dialogues derived from online shopping customer-feedback data.