  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 degrees. 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.
