We analyze the electrophoretic motion of a freely suspended closely fitting sphere, eccentrically positioned within an infinitely long cylindrical pore, when subjected to a uniform electric field acting parallel to the pore. The thin Debye-layer approximation is employed. Using singular perturbation expansions, the fluid domain is separated into an "inner" gap region around the sphere's equator, wherein electric field and velocity gradients are large, and an "outer" region, consisting of the remaining fluid domain, wherein field variations are moderate. Laplace's equation is solved within the gap region using stretched coordinates, whereby matching with the outer solution is facilitated by use of an integral conservation equation for the electric field flux. Using a reciprocal theorem, the electrokinetic contributions to the force (torque) on the sphere are represented as quadratures of the electric field over the sphere surface, with the respective stress fields pertaining to purely translational (rotational) motions appearing as Green's functions. The translational velocity of a concentrically positioned sphere is found to be half that for a sphere in an unbounded fluid. Both the translational and rotational sphere mobilities increase in magnitude with increasing eccentricity.