Imaging of cancer with 18F-fluorodeoxyglucose positron emission tomography (18F-FDG PET) has become a standard component of diagnosis and staging in oncology, and is becoming more important as a quantitative monitor of individual response to therapy. In this article we investigate the challenging problem of predicting a patient's response to neoadjuvant chemotherapy from a single 18F-FDG PET scan taken prior to treatment. We take a "radiomics" approach whereby a large amount of quantitative features is automatically extracted from pretherapy PET images in order to build a comprehensive quantification of the tumor phenotype. While the dominant methodology relies on hand-crafted texture features, we explore the potential of automatically learning low- to high-level features directly from PET scans. We report on a study that compares the performance of two competing radiomics strategies: an approach based on state-of-the-art statistical classifiers using over 100 quantitative imaging descriptors, including texture features as well as standardized uptake values, and a convolutional neural network, 3S-CNN, trained directly from PET scans by taking sets of adjacent intra-tumor slices. Our experimental results, based on a sample of 107 patients with esophageal cancer, provide initial evidence that convolutional neural networks have the potential to extract PET imaging representations that are highly predictive of response to therapy. On this dataset, 3S-CNN achieves an average 80.7% sensitivity and 81.6% specificity in predicting non-responders, and outperforms other competing predictive models.