The spin susceptibility of strongly correlated electrons in a low-disorder two-dimensional electron system exhibits a sharp increase tending to a divergence at a finite electron density. Surprisingly, this behavior is due to the divergence of the effective mass rather than that of the g-factor. Our results provide clear evidence for an interaction-induced phase transition to a new phase that may be a precursor phase or a direct transition to the long sought-after Wigner solid.. Properties of strongly correlated electrons confined in two dimensions are a forefront area of modern condensed matter physics. Two-dimensional (2D) electron systems can be realized on semiconductor surfaces (metal-insulator-semiconductor structures, heterostructures, and quantum wells); other examples include electrons on a surface of liquid helium or a single layer of carbon atoms (graphene). In some of these systems, Coulomb repulsion between electrons is small compared to the kinetic energy of electrons; such systems can be well described by Fermi liquid theory introduced by Landau in 1956.