Hyperspectral image analysis has become an important topic widely researched by the remote sensing community. Classification and segmentation of such imagery help understand the underlying materials within a scanned scene, since hyperspectral images convey a detailed information captured in a number of spectral bands. Although deep learning has established the state of the art in the field, it still remains challenging to train well-generalizing models due to the lack of ground-truth data. In this letter, we tackle this problem and propose an end-to-end approach to segment hyperspectral images in a fully unsupervised way. We introduce a new deep architecture which couples 3D convolutional autoencoders with clustering. Our multi-faceted experimental study---performed over benchmark and real-life data---revealed that our approach delivers high-quality segmentation without any prior class labels.