We investigate directly imaging exoplanets around eclipsing binaries using the eclipse as a natural tool for dimming the binary and thus increasing the planet to star brightness contrast. At eclipse, the binary becomes pointlike, making coronagraphy possible. We select binaries where the planet-star contrast would be boosted by >10x during eclipse, making it possible to detect a planet that is greater than or similar to 10x fainter or in a star system that is similar to 2-3x more massive than otherwise. Our approach will yield insights into planet occurrence rates around binaries versus individual stars. We consider both self-luminous (SL) and reflected light (RL) planets. In the SL case, we select binaries whose age is young enough so that an orbiting SL planet would remain luminous; in U Cep and AC Sct, respectively, our method is sensitive to SL planets of similar to 4.5 and similar to 9M(J)with current ground- or near-future space-based instruments and similar to 1.5 and similar to 6M(J)with future ground-based observatories. In the RL case, there are three nearby (less than or similar to 50 pc) systems-V1412 Aql, RR Cae, and RT Pic-around which a Jupiter-like planet at a planet-star separation of greater than or similar to 20 mas might be imaged with future ground- and space-based coronagraphs. A Venus-like planet at the same distance might be detectable around RR Cae and RT Pic. A habitable Earth-like planet represents a challenge; while the planet-star contrast at eclipse and planet flux are accessible with a 6-8 m space telescope, the planet-star separation is 1/3-1/4 of the angular separation limit of modern coronagraphy.