Open Radio Access Network (O-RAN) enables flexible and programmable RAN control through xApps running on the near-real-time RAN Intelligent Controller (Near-RT RIC). Traffic analysis and classification are essential functions in ORAN, supporting traffic-aware scheduling, QoS enforcement, and security control. Recent studies employ machine learning (ML)-based xApps to improve classification accuracy. However, they overlook inference latency, despite operating within latencysensitive RAN control loops. We present xChain, a multi-stage framework for traffic analysis and classification in O-RAN that jointly addresses latency and accuracy. xChain decomposes processing into a lightweight first stage and a specialized second stage. The first stage performs rapid traffic analysis and preprocessing to extract informative characteristics that facilitate more effective inference by specialized ML models in the second stage. We implement x Chain on FlexRIC integrated with OpenAirInterface (OAI) and evaluate it on a practical testbed. Within xChain, we propose and implement a lightweight traffic classification scheme, FastInfer, and incorporate an improved version of TRACTOR, a notable state-of-the-art scheme. Results show that FastInfer reduces inference latency by 6 × compared to the improved TRACTOR. Meanwhile, FastInfer maintains comparable overall classification accuracy, while significantly outperforming the improved TRACTOR for high-throughput traffic. Enabled by its multi-stage design, xChain provides a flexible foundation for diverse ML-based xApps supporting traffic analysis and classification in O-RAN.