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.
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