This Letter presents the first results of an observational campaign to study the Galactic center with INTEGRAL, the International Gamma-Ray Astrophysics Laboratory. Mosaicked images were constructed using data obtained with ISGRI, the soft gamma-ray instrument of the coded aperture IBIS imager, in the energy ranges 20-40 and 40-100 keV. These give a yet unseen view of the high-energy sources of this region in hard X-rays and gamma rays with an angular resolution of 12' (FWHM). We report on the discovery of a source, IGR J1745.6-2901, coincident with the Galactic nucleus Sgr A* to within 0farcm9. Located at R.A. = 17h45m38fs5 (J2000.0), decl. = -29°01'15'' (J2000.0), the source is visible up to about 100 keV with a 20-100 keV luminosity at 8 kpc of (2.89 ± 0.41) × 1035 ergs s-1. Although the new INTEGRAL source cannot unequivocally be associated to the Galactic nucleus, this is the first report of significant hard X-ray emission from within the inner 10' of the Galaxy and a contribution from the Galactic supermassive black hole itself cannot be excluded.