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 point-like, making coronagraphy possible. We select binaries where the planet-star contrast would be boosted by $>10times$ during eclipse, making it possible to detect a planet that is $gtrsim10times$ fainter or in a star system that is $sim2$-$3times$ 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 $sim$4.5$M_J$ and $sim$9$M_J$ with current ground- or near-future space-based instruments, and $sim$1.5$M_J$ and $sim$6$M_J$ with future ground-based observatories. In the RL case, there are three nearby ($lesssim50$ pc) systems -- V1412 Aql, RR Cae, RT Pic -- around which a Jupiter-like planet at a planet-star separation of $gtrsim20$ 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 6-8m space telescope, the planet-star separation is 1/3 - 1/4 of the angular separation limit of modern coronagraphy.
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