Eye movement biometrics (EMB) is a relatively recent behavioral biometric modality that may have the potential to become the primary authentication method in virtual- and augmented-reality devices due to their emerging use of eye-tracking sensors to enable foveated rendering techniques. However, existing EMB models have yet to demonstrate levels of performance that would be acceptable for real-world use. Deep learning approaches to EMB have largely employed plain convolutional neural networks (CNNs), but there have been many milestone improvements to convolutional architectures over the years including residual networks (ResNets) and densely connected convolutional networks (DenseNets). The present study employs a DenseNet architecture for end-to-end EMB and compares the proposed model against the most relevant prior works. The proposed technique not only outperforms the previous state of the art, but is also the first to approach a level of authentication performance that would be acceptable for real-world use.