Saturn's moon Titan shows landscapes with fluvial features suggestive of hydrology based on liquid methane. Recent efforts in understanding Titan's methane hydrological cycle have focused on occasional cloud outbursts near the south pole or cloud streaks at southern mid-latitudes and the mechanisms of their formation. It is not known, however, if the clouds produce rain or if there are also non-convective clouds, as predicted by several models. Here we show that the in situ data on the methane concentration and temperature profile in Titan's troposphere point to the presence of layered optically thin stratiform clouds. The data indicate an upper methane ice cloud and a lower, barely visible, liquid methane-nitrogen cloud, with a gap in between. The lower, liquid, cloud produces drizzle that reaches the surface. These non-convective methane clouds are quasi-permanent features supported by the global atmospheric circulation, indicating that methane precipitation occurs wherever there is slow upward motion. This drizzle is a persistent component of Titan's methane hydrological cycle and, by wetting the surface on a global scale, plays an active role in the surface geology of Titan.