The observation of the growth with time of chiral C* nuclei (domains) in the surrounding chiral nematic melt is presented for ferroelectric substances possessing the first order phase transition chiral nematic N* - chiral smectic C*, which is characterized by a strong jump of the tilt angle at the phase transition temperature. For the first time we report the observations of ferroelectric domains, having a 'screw' shape in the cell bulk; the domains grow much faster along the screw axis than across it. The screw pitch is appreciably larger than the helix pitch in the C* phase: the axis of the intrinsic helix turned out to be parallel to the screw axis. Both the screw- and the helix pitches were observed by optical microscopy. We provide a model, giving our interpretation of the phenomenon, based on the fundamental properties of the ferroelectric smectic C* phase at interfaces with various media. It was shown earlier that, due to the specific features of the surface tension of the ferroelectric smectic material, the smectic layers must be inclined with respect to the surface normal, and such an inclination is a function of the material parameters (for instance, the piezoelectric modulus), of the interface parameters (for instance, the anchoring strength) and of the temperature. In fact, the inclination of the smectic layers is related to the appearance of dislocation nets and depends on the interface anisotropy. We describe the growth of the smectic C*/N* interface, which is stabilized by free ions, decreasing the surface tension due to the neutralization of the polarization charges. The estimates of the inclination angle and of the ratio between the screw- and the intrinsic helix pitch are given.