Functional magnetic resonance imaging has a potential to provide insight into early detectors or biomarkers for various neurological disorders. With the advent of recent developments in deep learning, it may be possible to extract detailed information from neuroimaging data that is difficult to acquire using traditional techniques. Here we propose one such deep learning approach that makes use of a 3D Convolutional Neural Network to predict the onset of Alzheimer's disease even in a single subject based on resting state fMRI data. This approach extracts both spatial and temporal features from the 4D volume and eliminates the traditional complicated steps of feature extraction. In our experiments, a relatively simple deep learning architecture yields high performance in Alzheimer's disease classification. This illustrates the possibility of using volumetric feature extractors and classifiers as a tool to obtain biomarkers for neurological disorders and another step towards use of clinical fMRI.