We acquired observations of a partial transit of Kepler-167e, a Jupiter-analog exoplanet on a 1,071-day orbit, well beyond its water ice line, with the Spitzer Space Telescope. The timing of the Spitzer transit is consistent with the ephemeris measured from the two transits observed previously by the Kepler Space Telescope. The Spitzer observation rules out the existence of transit timing variations (TTVs) of order hours to days that are known to exist for other long-period exoplanets. Such TTVs render transit follow-up efforts intractable due to the substantial observing time required and the high risk of non-detection. For Kepler-167e, however, we are now able to predict future transit times through the anticipated era of the James Webb Space Telescope with uncertainties of less than six minutes. We interpret the lack of TTVs as an indication that Kepler-167e either does not have an exterior massive companion or that the gravitational interactions with any companions are below our detection threshold. We also measure Kepler-167es 3.6-$mu$m transit depth and use exoplanet and solar system models to make predictions about its transmission spectrum. The transiting nature of Kepler-167e and its similarity to Jupiter make it a unique and exceptional target for follow-up atmospheric characterization. Kepler-167e falls into a truly rare category among transiting exoplanets, and with a precisely constrained transit ephemeris, it is poised to serve as a benchmark in comparative investigations between exoplanets and the solar system.
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