We present theoretical calculations for the differential distribution of stellar orbital eccentricity in a galaxy halo , assuming that the stars constitute a spherical , collisionless system in dynamical equilibrium with a dark matter halo . In order to define the eccentricity e of a halo star for given energy E and angular momentum L , we adopt two types of gravitational potential , such as an isochrone potential and a Navarro-Frenk-White potential , that could form two ends covering in-between any realistic potential of dark matter halo . Based on a distribution function of the form f ( E,L ) that allows constant anisotropy in velocity dispersions characterized by a parameter \beta , we find that the eccentricity distribution is a monotonically increasing function of e for the case of highly radially anisotropic velocity dispersions ( \beta \gtrsim 0.6 ) , while showing a hump-like shape for the cases from radial through tangential velocity anisotropy ( \beta \lesssim 0.6 ) . We also find that when the velocity anisotropy agrees with that observed for the Milky Way halo stars ( \beta \simeq 0.5 - 0.7 ) , a nearly linear eccentricity distribution of N ( e ) \propto e results at e \lesssim 0.7 , largely independent of the potential adopted . Our theoretical eccentricity distribution would be a vital tool of examining how far out in the halo the dynamical equilibrium has been achieved , through comparison with kinematics of halo stars sampled at greater distances . Given that large surveys of the SEGUE and Gaia projects would be in progress , we discuss how our results would serve as a new guide in exploring the formation and evolution of the Milky Way halo .