Resting-state functional MRI (rs-fMRI) scans hold the potential to serve as a diagnostic or prognostic tool for a wide variety of conditions, such as autism, Alzheimer's disease, and stroke. While a growing number of studies have demonstrated the promise of machine learning algorithms for rs-fMRI based clinical or behavioral prediction, most prior models have been limited in their capacity to exploit the richness of the data. For example, classification techniques applied to rs-fMRI often rely on region-based summary statistics and/or linear models. In this work, we propose a novel volumetric Convolutional Neural Network (CNN) framework that takes advantage of the full-resolution 3D spatial structure of rs-fMRI data and fits non-linear predictive models. We showcase our approach on a challenging large-scale dataset (ABIDE, with N > 2,000) and report state-of-the-art accuracy results on rs-fMRI-based discrimination of autism patients and healthy controls.