We know from tree rings and other natural drought records that the western United States has been affected by several 'megadroughts' during the past millennium. But are these exceptionally long-lasting droughts due to unusual external forcings, or are they inevitable given a sufficiently long period of time? Here we present a statistical model that combines sea surface temperature records and drought severity statistics from the western USA, and use that tool to set out an expectation for megadrought, given no other changes in the climate system. Even though this model was trained using only modern climate data (and incorporates no information from tree rings or other proxies), it still produced megadroughts. Moreover, those simulated megadroughts were just as long-lasting, covered as large an area, and were just as severe as real megadroughts estimated from tree rings. That result means that megadroughts can occur in the western United States even if nothing else changes in the climate -- they really are just a matter of time. On the other hand, the only aspect of real-world megadroughts that the model cannot duplicate was the high number of these events during the so-called Medieval Climate Anomaly (800 to 1300 CE). So that cluster of megadroughts may have been caused by some sort of unusual climate circumstances that have not been observed by us during the past few decades. The proxy record tells us that many different kinds of exceptional or unusual climate events happened in the past. But it is often difficult to determine what caused those exceptional events because even, within a period of a thousand years, we still have very few cases. So besides being an aid to understand the causes of past megadroughts, we hope this approach can be applied to other paleoclimate records to distinguish between real interrelations between separate components of the climate system and simple coincidences.