In this work, we address the problem of image-goal navigation in the context of visually-realistic 3D environments. This task involves navigating to a location indicated by a target image in a previously unseen environment. Earlier attempts, including RL-based and SLAM-based approaches, have either shown poor generalization performance, or are heavily-reliant on pose/depth sensors. We present a novel method that leverages a cross-episode memory to learn to navigate. We first train a state-embedding network in a self-supervised fashion, and then use it to embed previously-visited states into a memory. In order to avoid overfitting, we propose to use data augmentation on the RGB input during training. We validate our approach through extensive evaluations, showing that our data-augmented memory-based model establishes a new state of the art on the image-goal navigation task in the challenging Gibson dataset. We obtain this competitive performance from RGB input only, without access to additional sensors such as position or depth.