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Competitive Self-Play (CSP) based Multi-Agent Reinforcement Learning (MARL) has shown phenomenal breakthroughs recently. Strong AIs are achieved for several benchmarks, including Dota 2, Glory of Kings, Quake III, StarCraft II, to name a few. Despite the success, the MARL training is extremely data thirsty, requiring typically billions of (if not trillions of) frames be seen from the environment during training in order for learning a high performance agent. This poses non-trivial difficulties for researchers or engineers and prevents the application of MARL to a broader range of real-world problems. To address this issue, in this manuscript we describe a framework, referred to as TLeague, that aims at large-scale training and implements several main-stream CSP-MARL algorithms. The training can be deployed in either a single machine or a cluster of hybrid machines (CPUs and GPUs), where the standard Kubernetes is supported in a cloud native manner. TLeague achieves a high throughput and a reasonable scale-up when performing distributed training. Thanks to the modular design, it is also easy to extend for solving other multi-agent problems or implementing and verifying MARL algorithms. We present experiments over StarCraft II, ViZDoom and Pommerman to show the efficiency and effectiveness of TLeague. The code is open-sourced and available at https://github.com/tencent-ailab/tleague_projpage