  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.
