The IRAM Interferometer has been used to detect the submillimeter source HDF 850.1 found by Hughes et al . ( 1998 ) in the Hubble Deep Field . The flux density measured at 1.3 mm ( 236 GHz ) is 2.2 \pm 0.3 ( 1 \sigma ) mJy , in agreement with the flux density measured at the JCMT . The flux densities and upper limits measured at 3.4 , 2.8 , 1.3 , 0.85 , and 0.45 mm show that the emission comes from dust . We suggest that the 1.3 mm dust source is associated with the optical arc-like feature , 3-593.0 , that has a photometric redshift z \approx 1.7 . If the HDF 850.1 is at this redshift and unlensed , its spectral energy distribution , combined with that of 3-593.0 , matches closely that of the ultraluminous galaxy VII Zw 31 . Another possibility is that the dust source may be gravitationally lensed by the elliptical galaxy 3-586.0 at z \approx 1 . The position of the dust source agrees within the errors with that of the tentative VLA radio source 3651+1226 .