Synchrotron-based time-resolved small-angle X-ray scattering was used to measure the early-stage spinodal decomposition kinetics in a highly viscous semidilute solution of polystyrene in dioctyl phthalate. Although strong nonlinearities in the kinetics were observed, a linear theory analysis could fit the evolution of the structure factor at short times and low wavenumbers. Nonlinearities become significant earlier at higher wavenumbers, which is consistent with recent computer simulation studies. From the linear theory analysis, the exponential relaxation rate of the structure factor R(q) was found to be linear in q(2) in the low-wavenumber region of the experiments, in agreement with mean-field theory for spinodal decomposition in polymer solutions. The wavenumber-dependent Onsager transport coefficient Lambda(q), which is the Fourier transform of the nonlocal mobility in a polymer system, was determined to scale as q(-4). This q dependence, which is stronger than that predicted by existing theory, may be related to entanglement effects.