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We present DELIGHT, or Deep Learning Identification of Galaxy Hosts of Transients, a new algorithm designed to automatically and in real time identify the host galaxies of extragalactic transients. The proposed algorithm receives as input compact, multiresolution images centered at the position of a transient candidate and outputs two-dimensional offset vectors that connect the transient with the center of its predicted host. The multiresolution input consists of a set of images with the same number of pixels, but with progressively larger pixel sizes and fields of view. A sample of 16,791 galaxies visually identified by the Automatic Learning for the Rapid Classification of Events broker team was used to train a convolutional neural network regression model. We show that this method is able to correctly identify both relatively large (10″ <r< 60″) and small (r≤ 10″) apparent size host galaxies using much less information (32 kB) than with a large, single-resolution image (920 kB). The proposed method has fewer catastrophic errors in recovering the position and is more complete and has less contamination (<0.86%) recovering the crossmatched redshift than other state-of-the-art methods. The more efficient representation provided by multiresolution input images could allow for the identification of transient host galaxies in real time, if adopted in alert streams from new generation of large -etendue telescopes such as the Vera C. Rubin Observatory.