A key component of characterizing multi-planet exosystems is testing the orbital stability based on the observed properties . Such characterization not only tests the validity of how observations are interpreted but can also place additional constraints upon the properties of the detected planets . The Kepler mission has identified hundreds of multi-planet systems but there are a few that have additional non-transiting planets and also have well characterized host stars . Kepler-68 is one such system for which we are able to provide a detailed study of the orbital dynamics . We use the stellar parameters to calculate the extent of the Habitable Zone for this system , showing that the outer planet lies within that region . We use N-body integrations to study the orbital stability of the system , in particular placing an orbital inclination constraint on the outer planet of i > 5 \arcdeg . Finally , we present the results of an exhaustive stability simulation that investigates possible locations of stable orbits for an Earth-mass planet . We show that there are several islands of stability within the Habitable Zone that could harbor such a planet , most particularly at the 2:3 mean motion resonance with the outer planet .