Abstract. Methane (CH₄) is the second strongest anthropogenic greenhouse gas after carbon dioxide (CO₂) and is responsible for about 20 % of the warming induced by long-lived greenhouse gases since pre-industrial times. Oxidation by the hydroxyl radical (OH) is the dominant atmospheric sink for methane, contributing to approximately 90 % of the total methane loss. Chemical losses by reaction with atomic oxygen (O¹D) and chlorine radicals (Cl) in the stratosphere are other sinks, contributing about 3 % to the total methane destruction. Moreover, the reaction with Cl is very fractionating, thus it has a much larger impact on δ¹³C-CH₄ than the reaction with OH. In this paper, we assess the impact of atomic Cl on atmospheric methane mixing ratios, methane atmospheric loss and atmospheric δ¹³C-CH₄. The offline version of the Global Circulation Model (GCM) LMDz, coupled to a chemistry module including the major methane chemical reactions, is run to simulate CH₄ concentrations and δ¹³C-CH₄ at the global scale. Atmospheric methane sink by Cl atoms in the stratosphere is found to be 7.32 ± 0.16 Tg/yr. Methane observations from vertical profiles obtained using AirCore samplers above 11 different locations across the globe and balloon measurements of δ¹³C-CH₄ and methane are used to assess the impact of the Cl sink in the chemistry transport model. Above 10 km, the presence of Cl in the model is found to have only a small impact on the vertical profile of total methane but a major influence on δ¹³C-CH₄ values, significantly improving the agreement between simulations and available observations. Stratospheric Cl is also found to have a substantial impact on surface δ¹³C-CH₄ values, leading to a difference of +0.27 ‰ (less negative values) after a 19-year run. As a result, this study suggests that the Cl sink needs to be properly taken into account (magnitude and trends) in order to better understand trends in the atmospheric δ¹³C-CH₄ signal when using atmospheric chemistry transport models for forward or inverse calculations.