Double ionization of the helium atom by slow electron impact (E(0)=106 eV) is studied in a kinematically complete experiment. Because of a low excess energy E(exc)=27 eV above the double ionization threshold, a strongly correlated three-electron continuum is realized. This is demonstrated by measuring and calculating the fully differential cross sections for equal energy sharing of the final-state electrons. While the electron emission is dominated by a strong Coulomb repulsion, also signatures of more complex dynamics of the full four-body system are identified.