Icosahedrite, natural icosahedral Al63Cu24Fe13, was discovered in a meteorite about 15 years ago. We have carried out a high-resolution X-ray diffraction study on a sample of this meteoritic mineral at the ESRF. The diffraction pattern turned out to be identical to an intermediate phase observed in synthetic i-AlCuFe during the transformation from the quasicrystalline state to a periodic rhombohedral phase. This particular natural Al63Cu24Fe13 grain is an icosahedral quasicrystal on which a modulation by six cosine waves propagating along the fivefold axes is superimposed, with a wavelength of about 20 nm and a polarization in the phason/perpendicular space. By examining the thermodynamic conditions for producing this modulated icosahedral phase at high pressure in the laboratory, we may gain insights into the formation process of the Khatyrka meteorite.