We present deformable unsupervised medical image registration using a randomly-initialized deep convolutional neural network (CNN) as regularization prior. Conventional registration methods predict a transformation by minimizing dissimilarities between an image pair. The minimization is usually regularized with manually engineered priors, which limits the potential of the registration. By learning transformation priors from a large dataset, CNNs have achieved great success in deformable registration. However, learned methods are restricted to domain-specific data and the required amounts of medical data are difficult to obtain. Our approach uses the idea of deep image priors to combine convolutional networks with conventional registration methods based on manually engineered priors. The proposed method is applied to brain MRI scans. We show that our approach registers image pairs with state-of-the-art accuracy by providing dense, pixel-wise correspondence maps. It does not rely on prior training and is therefore not limited to a specific image domain.