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Imaging atmospheric Cherenkov telescopes (IACTs), including the Cherenkov Telescope Array (CTA), detect images of the atmospheric showers generated by gamma rays and cosmic rays as they are absorbed by the atmosphere. Background cosmic rays greatly outnumber gamma rays, so correct classification of the detected images is critical for maximizing IACT sensitivity. I am exploring new event classification methods for CTA using convolutional neural networks, a class of deep learning algorithms specialized for image analysis. Unlike existing analysis methods, convolutional networks can extract useful features directly from images without having to define a preset parametrization. Initial studies using convolutional networks for gamma/hadron classification show promising performance.