© 2015 American Physical Society. Zero- to ultralow-field nuclear magnetic resonance (ZULF NMR) provides a new regime for the measurement of nuclear spin-spin interactions free from the effects of large magnetic fields, such as truncation of terms that do not commute with the Zeeman Hamiltonian. One such interaction, the magnetic dipole-dipole coupling, is a valuable source of spatial information in NMR, though many terms are unobservable in high-field NMR, and the coupling averages to zero under isotropic molecular tumbling. Under partial alignment, this information is retained in the form of so-called residual dipolar couplings. We report zero- to ultralow-field NMR measurements of residual dipolar couplings in acetonitrile-2-C13 aligned in stretched polyvinyl acetate gels. This permits the investigation of dipolar couplings as a perturbation on the indirect spin-spin J coupling in the absence of an applied magnetic field. As a consequence of working at zero magnetic field, we observe terms of the dipole-dipole coupling Hamiltonian that are invisible in conventional high-field NMR. This technique expands the capabilities of zero- to ultralow-field NMR and has potential applications in precision measurement of subtle physical interactions, chemical analysis, and characterization of local mesoscale structure in materials.