Measurements of one-dimensional Coulomb drag between adjacent edge states of quantum spin Hall insulators that are separated by an air gap suggest that quantum spin Hall effects could be used to suppress the impact of Coulomb interactions on the performance of future nanocircuits. Strong electron-electron interactions between adjacent nanoscale wires can lead to one-dimensional Coulomb drag, where current in one wire induces a voltage in the second wire via Coulomb interactions. This effect creates challenges for the development of nanoelectronic devices. Quantum spin Hall (QSH) insulators are a promising platform for the development of low-power electronic devices due to their topological protection of edge states from non-magnetic disorder. However, although Coulomb drag in QSH edges has been considered theoretically, experimental explorations of the effect remain limited. Here, we show that one-dimensional Coulomb drag can be observed between adjacent QSH edges that are separated by an air gap. The pair of one-dimensional helical edge states is created in split H-bar devices in inverted InAs/GaSb quantum wells. Near the Dirac point, negative drag signals dominate at low temperatures and exhibit a non-monotonic temperature dependence, suggesting that distinct drag mechanisms compete and cancel out at higher temperatures. The results suggest that QSH effects could be used to suppress the impact of Coulomb interactions on the performance of future nanocircuits.