Hydroclimate variability of the southwest United States (SWUS) is influenced by the tropical Pacific Ocean, particularly the phase of the El Niño/Southern Oscillation (ENSO), via teleconnections, which are expected to be altered by climate change. However, natural variability in this teleconnection has not been robustly quantified, complicating the detection of anthropogenic climate change. Here, we use a linear inverse model (LIM) to quantify natural variability in the ENSO-SWUS teleconnection. The LIM yields realistic teleconnection patterns with century-scale variability in teleconnection strength comparable to simulations from the Last Millennium Ensemble project and the Coupled Model Intercomparison Project Phases 5 and 6. The variability quantified by the LIM illuminates two aspects of our understanding of ENSO and its impacts: the inherent statistics of the observable system can produce century-long periods of nonsignificant correlation, and detecting changes in ENSO-related hydroclimate variability is challenging in a changing climate.