Solar gravity modes have been actively sought because they directly probe the solar core (below 0.2 solar radius), but they have not been conclusively detected in the Sun because of their small surface amplitudes. Using data from the Global Oscillation at Low Frequency instrument, we detected a periodic structure in agreement with the period separation predicted by the theory for gravity dipole modes. When studied in relation to simulations including the best physics of the Sun determined through the acoustic modes, such a structure favors a faster rotation rate in the core than in the rest of the radiative zone.