Contrastive self-supervised learning has emerged as a promising approach to unsupervised visual representation learning. In general, these methods learn global (image-level) representations that are invariant to different views (i.e., compositions of data augmentation) of the same image. However, many visual understanding tasks require dense (pixel-level) representations. In this paper, we propose View-Agnostic Dense Representation (VADeR) for unsupervised learning of dense representations. VADeR learns pixelwise representations by forcing local features to remain constant over different viewing conditions. Specifically, this is achieved through pixel-level contrastive learning: matching features (that is, features that describes the same location of the scene on different views) should be close in an embedding space, while non-matching features should be apart. VADeR provides a natural representation for dense prediction tasks and transfers well to downstream tasks. Our method outperforms ImageNet supervised pretraining (and strong unsupervised baselines) in multiple dense prediction tasks.