The time delay between multiple images of strongly lensed quasars is a powerful tool for measuring the Hubble constant (H0). To achieve H0 measurements with higher precision and accuracy using the time delay, it is crucial to expand the sample of lensed quasars. We conduct a search for strongly lensed quasars in the Dark Energy Spectroscopic Instrument (DESI) Legacy Imaging Surveys. The DESI Legacy Surveys comprise 19000deg^2^ of the extragalactic sky observed in three optical bands (g, r, and z), making it well suited for the discovery of new strongly lensed quasars. We apply an autocorrelation algorithm to ~5 million objects classified as quasars in the DESI Quasar Sample. These systems are visually inspected and ranked. Here, we present 436 new multiply lensed and binary quasar candidates, 65 of which have redshifts from Sloan Digital Sky Survey Data Release 16. We provide redshifts for an additional 18 candidates from the SuperNova Integral Field Spectrograph.