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Following the recent detection of HCl in the atmosphere of Mars by ExoMars/Trace Gas Orbiter, we present here the first measurement of the 37Cl/35Cl isotopic ratio in the Martian atmosphere using a set of Nadir Occultation for MArs Discovery (NOMAD) observations. We determine an isotopic anomaly of −6 ± 78‰ compared to Earth standard, consistent with the −51‰–−1‰ measured on Mars' surface by Curiosity. The measured isotopic ratio is also consistent with surface measurements, and suggests that Cl reservoirs may have undergone limited processing since formation in the Solar Nebula. The examination of possible sources and sinks of HCl shows only limited pathways to short‐term efficient Cl fractionation and many plausible reservoirs of "light" Cl. Plain Language Summary: Recently, HCl has been observed in the Martian atmosphere for the first time by the instruments onboard the European Space Agency (ESA) ExoMars Trace Gas Orbiter. This discovery implies that there is an active chemical and physical cycle of chlorine in the Martian atmosphere. The Cl in HCl is usually present with its two stable main isotopes, the "light" 35Cl and "heavy" 37Cl, their ratio in chlorine‐bearing compounds is variable across the Solar System, and can be revealing of the chemistry at play, surface‐atmosphere interactions and the degree of evolution of chlorine reservoirs. In this work, we measure the 37Cl to 35Cl ratio for the first time in the Martian atmosphere. In average, we find that the measured atmospheric value is slightly "lighter" than the standard value at Earth (although with large uncertainty), and consistent with that measured at Mars' surface. This indicates that Cl does not actively escape from the Martian atmosphere, and that the Cl chemistry at Mars has little efficiency in changing the isotopic signature of Cl, if at all. The "light" Cl isotopic composition of surface and atmosphere may indicate that Cl reservoirs on Mars are less processed than other bodies in the Solar System. Key Points: Cl isotopic ratio in atmospheric HCl on Mars is measured with Nadir Occultation for MArs Discovery (NOMAD), finding a slight depletion of 37Cl compared to Earth standardThe atmospheric Cl isotopic ratio is compatible with surface values measured by Mars Science Laboratory (MSL), not showing any fractionation beyond uncertaintiesThe majority of possible HCl depletion processes at Mars yield residual HCl with lighter Cl than its source [ABSTRACT FROM AUTHOR]