Water is not currently stable in liquid form on the martian surface due to the present mean atmospheric pressure of similar to 7 mbar and mean global temperature of similar to 220 K. However, geomorphic features and hydrated mineral assemblages suggest that Mars' climate was once warmer and liquid water flowed on the surface. These observations may indicate a substantially more massive atmosphere in the past, but there have been few observational constraints on paleoatmospheric pressures. Here we show how the Ar-40/Ar-36 ratios of trapped gases within martian meteorite ALH 84001 constrain paleoatmospheric pressure on Mars during the Noachian era [similar to 4.56-3.8 billion years (Ga)]. Our model indicates that atmospheric pressures did not exceed similar to 1.5 bar during the first 400 million years (Ma) of the Noachian era, and were <400 mbar by 4.16 Ga. Such pressures of CO2 are only sufficient to stabilize liquid water on Mars' surface at low latitudes during seasonally warm periods. Other greenhouse gases like SO2 and water vapor may have played an important role in intermittently stabilizing liquid water at higher latitudes following major volcanic eruptions or impact events. (C) 2012 Elsevier Inc. All rights reserved.