  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 $>10\times$ during eclipse, making it possible to detect a
planet that is $\gtrsim10\times$ fainter or in a star system that is
$\sim2$-$3\times$ 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.
