Two-neutrino double electron capture ($2 u$ECEC) is a second-order Weak process with predicted half-lives that surpass the age of the Universe by many orders of magnitude. Until now, indications for $2 u$ECEC decays have only been seen for two isotopes, $^{78}$Kr and $^{130}$Ba, and instruments with very low background levels are needed to detect them directly with high statistical significance. The $2 u$ECEC half-life provides an important input for nuclear structure models and its measurement represents a first step in the search for the neutrinoless double electron capture processes ($0 u$ECEC). A detection of the latter would have implications for the nature of the neutrino and give access to the absolute neutrino mass. Here we report on the first direct observation of $2 u$ECEC in $^{124}$Xe with the XENON1T Dark Matter detector. The significance of the signal is $4.4sigma$ and the corresponding half-life $T_{1/2}^{2 utext{ECEC}} = (1.8pm 0.5_text{stat}pm 0.1_text{sys})times 10^{22};text{y}$ is the longest ever measured directly. This study demonstrates that the low background and large target mass of xenon-based Dark Matter detectors make them well suited to measuring other rare processes as well, and it highlights the broad physics reach for even larger next-generation experiments.