We propose a new probe of the dependence of the fine-structure constant α on a strong gravitational field using metal lines in the spectra of white-dwarf stars. Comparison of laboratory spectra with far-UV astronomical spectra from the white-dwarf star G191-B2B recorded by the Hubble Space Telescope Imaging Spectrograph gives limits of Δα/α=(4.2±1.6)×10(-5) and (-6.1±5.8)×10(-5) from FeV and NiV spectra, respectively, at a dimensionless gravitational potential relative to Earth of Δφ≈5×10(-5). With better determinations of the laboratory wavelengths of the lines employed these results could be improved by up to 2 orders of magnitude.