Convolutional architectures have recently been shown to be competitive on many sequence modelling tasks when compared to the de-facto standard of recurrent neural networks (RNNs) while providing computational and modelling advantages due to inherent parallelism. However, currently, there remains a performance gap to more expressive stochastic RNN variants, especially those with several layers of dependent random variables. In this work, we propose stochastic temporal convolutional networks (STCNs), a novel architecture that combines the computational advantages of temporal convolutional networks (TCN) with the representational power and robustness of stochastic latent spaces. In particular, we propose a hierarchy of stochastic latent variables that captures temporal dependencies at different time-scales. The architecture is modular and flexible due to the decoupling of the deterministic and stochastic layers. We show that the proposed architecture achieves state of the art log-likelihoods across several tasks. Finally, the model is capable of predicting high-quality synthetic samples over a long-range temporal horizon in modelling of handwritten text.