Coulomb drag experiments have been an essential tool to study strongly interacting lowdimensional systems. Historically, this effect has been explained in terms of momentum transfer between electrons in the active and the passive layer. Here, we report Coulomb drag measurements between laterally coupled GaAs/AlGaAs quantum wires in the multiple 1D sub-band regime that break Onsager's reciprocity upon both layer and current direction reversal, in contrast to prior 1D Coulomb drag results. The drag signal shows nonlinear I-V characteristics, which are well characterized by a third-order polynomial fit. These findings are qualitatively consistent with a rectified drag signal induced by charge fluctuations. However, the nonmonotonic temperature dependence of this drag signal suggests that strong electron-electron interactions, expected within the Tomonaga-Luttinger liquid framework, remain important and standard interaction models are insufficient to capture the qualitative nature of rectified 1D Coulomb drag.