Predicting the future in real-world settings, particularly from raw sensory observations such as images, is exceptionally challenging. Real-world events can be stochastic and unpredictable, and the high dimensionality and complexity of natural images requires the predictive model to build an intricate understanding of the natural world. Many existing methods tackle this problem by making simplifying assumptions about the environment. One common assumption is that the outcome is deterministic and there is only one plausible future which leads to low-quality predictions in real-world settings with stochastic dynamics. In contrast, we developed a variational stochastic method for video prediction that predicts a different possible future for each sample of its latent random variables. To the best of our knowledge, our model is the first to provide effective stochastic multi-frame prediction for real-world video. We demonstrate the capability of the proposed method in predicting detailed future frames of videos on multiple real-world datasets, both action-free and action-conditioned. We find that our proposed method produces substantially improved video predictions when compared to the same model without stochasticity, and to other stochastic video prediction methods. The TensorFlow-based implementation of our method will be open sourced upon publication.