We report extensive spectroscopic and differential V-band photometric observations of the 18.4 day detached double-lined eclipsing binary LV Her (F9 V), which has the highest eccentricity (e 0.613) among the systems with well-measured properties. We determine the absolute masses and radii of the components to be M ₁ = 1.193 ± 0.010 M _☉, M ₂ = 1.1698 ± 0.0081 M _☉, R ₁ = 1.358 ± 0.012 R _☉, and R ₂ = 1.313 ± 0.011 R _☉, with fractional errors of 0.9% or better. The effective temperatures are 6060 ± 150 K and 6030 ± 150 K, respectively, and the overall metallicity is estimated to be [m/H] = +0.08 ± 0.21. A comparison with current stellar evolution models for this composition indicates an excellent fit for an age between 3.8 and 4.2 Gyr, with both stars being near the middle of their main-sequence lifetimes. Full integration of the equations for tidal evolution is consistent with the high eccentricity, and suggests that the stars' spin axes are aligned with the orbital axis, and that their rotations should be pseudo-synchronized. The latter prediction is not quite in agreement with the measured projected rotational velocities.