The NASA Space Telescope (ST) is a 2.4-m aperture, f/24 Ritchey-Chretien telescope coupled to five on-board astronomical scientific packages. The very accurate line-of-sight stability required by ST during operating periods of up to 24 hours is maintained by the Pointing Control System whose optical system, the Fine Guidance Subsystem (FGS), is described. The Pointing Control System includes three identical FGSs, any two of which provide line-of-sight stabilization by tracking guide stars while the third performs astrometry. The optical design of each provides a well-corrected demagnified pupil at which the fine guidance field of view is scanned. Traditionally, field-aberration correction is performed by placing a refractive field group near the telescope image plane. Designs of this type are difficult to correct and complex, and require large and difficult-to-manufacture elements. The optical system for the ST FGS performs the field aberration correction within the FGS near a pupil plane measuring only 52.7 mm. The refractive group thus required is relatively small and easily manufactured. The design, up to that pupil plane, consists of a collimating mirror located after the telescope image and a five-element refractive group placed just before the pupil plane. The design is simple and easily corrected, and offers substantial advantages over the traditional approach in terms of manufacturability.