Training large deep learning models at scale is very challenging. This paper proposes Chimera, a novel pipeline parallelism scheme which combines bidirectional pipelines for efficiently training large-scale models. Chimera is a synchronous approach and therefore no loss of accuracy, which is more convergence-friendly than asynchronous approaches. Compared with the latest synchronous pipeline approach, Chimera reduces the number of bubbles by up to 50%; benefiting from the sophisticated scheduling of bidirectional pipelines, Chimera has a more balanced activation memory consumption. Evaluations are conducted on Transformer based language models. For a GPT-2 model with 1.3 billion parameters running on 2,048 GPU nodes of the Piz Daint supercomputer, Chimera improves the training throughput by 1.16x-2.34x over the state-of-the-art synchronous and asynchronous pipeline approaches.