A continuum of magnetic states has been observed by neutron scattering from the spin-1 chain compound CsNiCl3 in its disordered gapped one-dimensional phase. Results using both triple-axis and time-of-flight spectrometers show that around the antiferromagnetic point Qc = pi, the continuum lies higher in energy than the Haldane gapped excitations. At 6 K the integrated intensity of the continuum is about 12(2)% of the total spectral weight. This result is considerably larger than the 1%-3% weight predicted by the nonlinear sigma model for the three-particle continuum.