We investigate the evolution of the chemical potential of a two-dimensional electron system (2DES) as a function of density at a fixed magnetic field. By using a bilayer system, changes in the chemical potential of one 2DES are determined from the density variation induced in the second, nearby 2DES. At high magnetic fields around a filling factor of ν=1 or ν=2, the chemical potential jump associated with the condensation in a quantum Hall state exhibits two anomalies symmetrically located around these integer filling factors. They are attributed to the formation of a 2D Wigner crystal of quasiparticles.