We investigate the stability of idealized planetary systems consisting of five planets, each equal in mass to the Earth, orbiting a one solar mass star. All planets orbit in the same plane and in the same direction, and the planets are uniformly spaced in units of mutual Hill Sphere radii. However, in contrast to analogous studies by Smith and Lissauer (2009) and Obertas et al. (2017), we integrate systems where one or more planets begin on eccentric orbits, with eccentricities \(e\) as large as \(e=0.05\) being considered. For a given initial orbital separation, larger initial eccentricity of a single planet generally leads to shorter system lifetime, regardless of which planet is initially on an eccentric orbit. The approximate trend of instability times increasing exponentially with initial orbital separation of the planets found previously for planets with initially circular orbits is also present for systems with initially eccentric orbits. Mean motion resonances also tend to destabilize these systems, although the reductions in system lifetimes are not as large as for initially circular orbits. Systems with all planets having initial \(e=0.05\) and aligned periapse angles typically survive far longer than systems with the same spacing in initial semi-major axis and one planet with \(e=0.05\), but they have slightly shorter lifetimes than those with planets initially on circular orbits.