An exclusive measurement has been made of the Coulomb dissociation of the two-neutron halo nucleus 11Li at 70 MeV/nucleon at RIKEN. Strong low-energy (soft) E1 excitation is observed, peaked at about Ex = 0.6 MeV with B(E1) = 1.42(18) e2fm2 for Erel < or = 3 MeV, which was largely missed in previous measurements. This excitation represents the strongest E1 transition ever observed at such low excitation energies. The spectrum is reproduced well by a three-body model with a strong two-neutron correlation, which is further supported by the E1 non-energy-weighted cluster sum rule.