Inelastic neutron scattering measurements show the existence of a strong two-spinon continuum in the frustrated ferromagnetic spin-1/2 chain compound LiCuVO4. The dynamic magnetic susceptibility is well described by a mean-field model of two coupled interpenetrating antiferromagnetic Heisenberg chains. The extracted values of the exchange integrals are in good agreement with the static magnetic susceptibility data and an earlier spin-wave description of the bound state near the lower boundary of the two-spinon continuum. In addition, there is clear evidence for a four-spinon continuum at high energies.