  We present TYC 2505-672-1 as a newly discovered and remarkable eclipsing
system comprising an M-type red giant that undergoes a ~3.45 year long,
near-total eclipse (depth of ~4.5 mag) with a very long period of ~69.1 yr. TYC
2505-672-1 is now the longest-period eclipsing binary system yet discovered,
more than twice as long as that of the currently longest-period system,
$\epsilon$ Aurigae. We show from analysis of the light curve including both our
own data and historical data spanning more than 120 yr and from modeling of the
spectral energy distribution, both before and during eclipse, that the red
giant primary is orbited by a moderately hot source (T$_{eff}$~8000 K) that is
itself surrounded by an extended, opaque circumstellar disk. From the measured
ratio of luminosities, the radius of the hot companion must be in the range
0.1-0.5 Rsun (depending on the assumed radius of the red giant primary), which
is an order of magnitude smaller than that for a main sequence A star and 1-2
orders of magnitude larger than that for a white dwarf. The companion is
therefore most likely a "stripped red giant" subdwarf-B type star destined to
become a He white dwarf. It is however somewhat cooler than most sdB stars,
implying a very low mass for this "pre-He-WD" star. The opaque disk surrounding
this hot source may be a remnant of the stripping of its former hydrogen
envelope. However, it is puzzling how this object became stripped, given that
it is at present so distant (orbital semi-major axis of ~24 AU) from the
current red giant primary star. Extrapolating from our calculated ephemeris,
the next eclipse should begin in early UT 2080 April and end in mid UT 2083
September (eclipse center UT 2081 December 24). This system is poised to become
an exemplar of a very rare class of systems, even more extreme in several
respects than the well studied archetype $\epsilon$ Aurigae.
