The heaviest bound isotope of boron ^{19}B has been investigated using exclusive measurements of its Coulomb dissociation, into ^{17}B and two neutrons, in collisions with Pb at 220 MeV/nucleon. Enhanced electric dipole (E1) strength is observed just above the two-neutron decay threshold with an integrated E1 strength of B(E1)=1.64±0.06(stat)±0.12(sys) e^{2} fm^{2} for relative energies below 6 MeV. This feature, known as a soft E1 excitation, provides the first firm evidence that ^{19}B has a prominent two-neutron halo. Three-body calculations that reproduce the energy spectrum indicate that the valence neutrons have a significant s-wave configuration and exhibit a dineutronlike correlation.