By focusing a high intensity acoustic wave in liquid helium, we have observed the nucleation of solid helium inside the wave above a certain threshold in amplitude. The nucleation is a stochastic phenomenon. Its probability increases continuously from 0 to 1 in a narrow pressure interval around Pm + 4.7 bars (Pm is the melting pressure where liquid and solid helium are in equilibrium). This overpressure is larger by two to three orders of magnitude than what had been previously observed. Our result strongly supports a recent suggestion by Balibar, Mizusaki and Sasaki that, in all previous experiments, solid helium nucleated on impurities.