After an 11-year observing campaign, we present the combined visual-spectroscopic orbit of the formerly unremarkable bright star HR 7345 (HD 181655, HIP 94981, GJ 754.2). Using the Separated Fringe Packet method with the CHARA Array, we were able to determine a difficult-to-complete orbital period of 331.609+/-0.004 days. The 11-month period causes the system to be hidden from interferometric view behind the Sun for three years at a time. Due to the high-eccentricity orbit of about 90% of a year, after 2018 January the periastron phase will not be observable again until late 2021. Hindered by its extremely high eccentricity of 0.9322+/-0.0001, the double-lined spectroscopic phase of HR 7345 is observable for 15 days. Such a high eccentricity for HR 7345 places it among the most eccentric systems in catalogs of both visual and spectroscopic orbits. For this system, we determine nearly identical component masses of 0.941+/-0.076 M_{sun}_ and 0.926+/-0.075 M_{sun}_ as well as an orbital parallax of 41.08+/-0.77 mas.