We demonstrate a new NMR technique that is suitable for the measurement of weak proton dipolar interactions in fluid polymers where rapid segmental dynamics "preaverage" the rigid-lattice dipolar coupling. The method is especially applicable to polymer melts and networks, where such residual interactions can provide valuable insight regarding molecular order and reorientational dynamics. We use this method to study natural rubber under uniaxial stretching. By measuring the residual dipolar coupling and its orientation dependence, we are able to distinguish the influence of chain stretching from chain reorientation in the deformation process. The pulse sequence we employ directly generates a function beta, which is zero in the absence of dipolar interactions, which is completely independent of all Zeeman dephasing associated with chemical shifts or magnetic inhomogeneity, and whose time dependence can yield both the magnitude and the fluctuation rate of the residual dipolar interaction.