  <abridged> The large relative sizes of circumstellar and circumplanetary
disks imply that they might be seen in eclipse in stellar light curves. We
estimate that a survey of ~10^4 young (~10 Myr old) post-accretion pre-MS stars
monitored for ~10 years should yield at least a few deep eclipses from
circumplanetary disks and disks surrounding low mass companion stars. We
present photometric and spectroscopic data for a pre-MS K5 star (1SWASP
J140747.93-394542.6), a newly discovered ~0.9 Msun member of the ~16 Myr-old
Upper Cen-Lup subgroup of Sco-Cen at a kinematic distance of 128 pc. SuperWASP
and ASAS light curves for this star show a remarkably long, deep, and complex
eclipse event centered on 29 April 2007. At least 5 multi-day dimming events of
>0.5 mag are identified, with a >3.3 mag deep eclipse bracketed by two pairs of
~1 mag eclipses symmetrically occurring +-12 days and +-26 days before and
after. Hence, significant dimming of the star was taking place on and off over
at least a ~54 day period in 2007, and a strong >1 mag dimming event occurred
over a ~12 day span. We place a firm lower limit on the period of 850 days
(i.e. the orbital radius of the eclipser must be >1.7 AU and orbital velocity
must be <22 km/s). The shape of the light curve is similar to the lop-sided
eclipses of the Be star EE Cep. We suspect that this new star is being eclipsed
by a low-mass object orbited by a dense inner disk, girded by at least 3 dusty
rings of lower optical depth. Between these rings are at least two annuli of
near-zero optical depth (i.e. gaps), possibly cleared out by planets or moons,
depending on the nature of the secondary. For possible periods in the range
2.33-200 yr, the estimated total ring mass is ~8-0.4 Mmoon (if the rings have
optical opacity similar to Saturn's rings), and the edge of the outermost
detected ring has orbital radius ~0.4-0.09 AU.
