Deep neural networks (DNNs) are known for their vulnerability to adversarial examples. These are examples that have undergone small, carefully crafted perturbations, and which can easily fool a DNN into making misclassifications at test time. Thus far, the field of adversarial research has mainly focused on image models, under either a white-box setting, where an adversary has full access to model parameters, or a black-box setting where an adversary can only query the target model for probabilities or labels. Whilst several white-box attacks have been proposed for video models, black-box video attacks are still unexplored. To close this gap, we propose the first black-box video attack framework, called V-BAD. V-BAD utilizes tentative perturbations transferred from image models, and partition-based rectifications found by the NES on partitions (patches) of tentative perturbations, to obtain good adversarial gradient estimates with fewer queries to the target model. V-BAD is equivalent to estimating the projection of an adversarial gradient on a selected subspace. Using three benchmark video datasets, we demonstrate that V-BAD can craft both untargeted and targeted attacks to fool two state-of-the-art deep video recognition models. For the targeted attack, it achieves $>$93\% success rate using only an average of $3.4 \sim 8.4 \times 10^4$ queries, a similar number of queries to state-of-the-art black-box image attacks. This is despite the fact that videos often have two orders of magnitude higher dimensionality than static images. We believe that V-BAD is a promising new tool to evaluate and improve the robustness of video recognition models to black-box adversarial attacks.