The Hill-Clohessy-Wiltshire equations describe the motion of a deputy satellite in close proximity to a circular chief. This paper presents an extension of the Hill-Clohessy-Wiltshire equations to elliptic chiefs by a virtual-time approach. The relative position at each instant is approximated by evaluating the Hill-Clohessy-Wiltshire solution at a virtual time. Therefore, the shape of the trajectory is approximated using an Hill-Clohessy-Wiltshire trajectory, but the progress along the trajectory is modified to account for the chief's eccentricity. Example solutions for the virtual time are calculated, and the errors of the Hill-Clohessy-Wiltshire and virtual-time solutions are compared.