During the survey of the Galactic center region performed by the hard X-ray telescope SIGMA aboard the Granat space observatory, a persistent source coincident with the Terzan 1 globular cluster has been observed. This source may be associated with the persistent X-ray source X1732-304 studied by EXOSAT, ROSAT, and ART-P and with the X-ray burster source detected by Hakucho in Terzan 1. The source appears at the 5.5 σ level in the SIGMA images in the 40-75 keV energy range. There is no evidence for time variability, and the photon spectrum is reproduced by a thermal bremsstrahlung law with a temperature equal to 33+32-12 keV as well as by a power law with spectral index equal to -3.2±0.7. The luminosity in the 40-75 keV energy range is equal to 4.0±0.8 x 1035 ergs s-1, assuming a distance of 10 kpc. This hard X-ray emission may come from a low-mass X-ray binary with a neutron star as the compact member.