Muon spin rotation experiments on a stoichiometric sample of the non-Fermi liquid (NFL) heavy-fermion compound UCu_4Pd, in which recent neutron Bragg scattering measurements are consistent with an ordered structure, indicate that the U-ion susceptibility is strongly inhomogeneous at low temperatures. This suggests that residual disorder dominates NFL behavior. The data also indicate a short correlation length (lesssim 1 lattice spacing) for this inhomogeneity and a rapid low-temperature U-moment relaxation rate (gtrsim 10^{12} s^{-1}), which constrain cluster-based models of NFL behavior.