  Using Campaign 15 data from the K2 mission, we have discovered a
triply-eclipsing triple star system: EPIC 249432662. The inner eclipsing binary
system has a period of 8.23 days, with shallow $\sim$3% eclipses. During the
entire 80-day campaign, there is also a single eclipse event of a third-body in
the system that reaches a depth of nearly 50% and has a total duration of 1.7
days, longer than for any previously known third-body eclipse involving
unevolved stars. The binary eclipses exhibit clear eclipse timing variations. A
combination of photodynamical modeling of the lightcurve, as well as seven
follow-up radial velocity measurements, has led to a prediction of the
subsequent eclipses of the third star with a period of 188 days. A campaign of
follow-up ground-based photometry was able to capture the subsequent pair of
third-body events as well as two further 8-day eclipses. A combined
photo-spectro-dynamical analysis then leads to the determination of many of the
system parameters. The 8-day binary consists of a pair of M stars, while most
of the system light is from a K star around which the pair of M stars orbits.
