Binocular eye-gaze tracking can be used to estimate the point-of-gaze (POG) of a subject in real-world 3-D space using the vergence of the eyes. In this paper, a novel noncontact model-based technique for 3-D POG estimation is presented. The noncontact system allows people to select real-world objects in 3-D physical space using their eyes, without the need for head-mounted equipment. Remote 3-D POG estimation may be especially useful for persons with quadriplegia or Amyotrophic Lateral Sclerosis. It would also enable a user to select 3-D points in space generated by 3-D volumetric displays, with potential applications to medical imaging and telesurgery. Using a model-based POG estimation algorithm allows for free head motion and a single stage of calibration. It is shown that an average accuracy of 3.93 cm was achieved over a workspace volume of 30 x 23 x 25 cm (W x H x D) with a maximum latency of 1.5 s due to the digital filtering employed. The users were free to naturally move and reorient their heads while operating the system, within an allowable headspace of 3 cm x 9 cm x 14 cm.