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We report on a sub-stellar companion search utilizing interferometricfringe-tracking astrometry acquired with Fine Guidance Sensor 3 (FGS 3) on theHubble Space Telescope. Our targets were Proxima Centauri and Barnard's Star.We obtain absolute parallax values for Proxima Cen pi_{abs} = 0.7687 arcsecondand for Barnard's Star pi_{abs} = 0.5454 arcsecond.  Once low-amplitude instrumental systematic errors are identified and removed,our companion detection sensitivity is less than or equal to one Jupiter massfor periods longer than 60 days for Proxima Cen. Between the astrometry and theradial velocity results we exclude all companions with M > 0.8M_{Jup} for therange of periods 1 < P < 1000 days. For Barnard's Star our companion detectionsensitivity is less than or equal to one Jupiter mass for periods long er than150 days. Our null results for Barnard's Star are consistent with those ofGatewood (1995).Comment: 35 pages, 13 figures, to appear in August 1999 A

the astronomical journal

Interferometric Astrometry of Proxima Centauri and Barnard's Star Using [ITAL]HUBBLE SPACE TELESCOPE[/ITAL] Fine Guidance Sensor 3: Detection Limits for Substellar Companions