We have investigated the spin dynamics in the strongly correlated chain copper oxide SrCuO\(_2\) for energies up to \(\gtrsim 0.6\) eV using inelastic neutron scattering. We observe an acoustic band of magnetic excitations which is well described by the "Muller-ansatz" for the two-spinon continuum in the S=1/2 antiferromagnetic Heisenberg spin chain. The lower boundary of the continuum extends up to \(\approx 360\) meV, which corresponds to an exchange constant \(J = 226(12)\) meV. Our finding that an effective Heisenberg spin Hamlitonian adequately describes the spin sector of this 1D electron system, even though its energy scale is comparable to that of charge excitations, provides compelling experimental evidence for spin-charge separation.