Magnetic excitations of the quasi-1D S = 1/2 Heisenberg antiferromagnet (HAF) Cs2CuCl4 have beer measured as a function of magnetic field using neutron scattering. For T < 0.62 K and B = 0 T the weak interchain coupling produces 3D incommensurate ordering. Fields greater than B-c = 1.66 T, but less than the field (similar or equal to 8 T) required to fully align the spins, are observed to decouple the chains, and the system enters a disordered intermediate-field phase (IFP). The IFP excitations are in agreement with the predictions of Muller et al. for the 1D S = 1/2 HAF, and Talstra and Haldane for the related l/r(2) chain (the Haldane-Shastry model). This behavior is inconsistent with linear spin-wave theory.