Conditional Variational AutoEncoder (CVAE) is promising for modeling one-to-many relationships in dialogue generation, as it can naturally generate many responses from a given context. However, the conventional used continual latent variables in CVAE are more likely to generate generic rather than distinct and specific responses. To resolve this problem, we introduce a novel discrete variable called prior context which enables the generation of favorable responses. Specifically, we present Prior Context VAE (PCVAE), a hierarchical VAE that learns prior context from data automatically for dialogue generation. Meanwhile, we design Active Codeword Transport (ACT) to help the model actively discover potential prior context. Moreover, we propose Autoregressive Compatible Arrangement (ACA) that enables modeling prior context in autoregressive style, which is crucial for selecting appropriate prior context according to a given context. Extensive experiments demonstrate that PCVAE can generate distinct responses and significantly outperforms strong baselines.