Radiometric dating with 39Ar covers a unique time span and offers key advances in interpreting environmental archives of the last millennium. Although this tracer has been acknowledged for decades, studies so far have been limited by the low abundance and radioactivity, thus requiring huge sample sizes. Atom trap trace analysis, an application of techniques from quantum physics such as laser cooling and trapping, allows us to reduce the sample volume by several orders of magnitude compared with conventional techniques. Here we show that the adaptation of this method to 39Ar is now available for glaciological applications, by demonstrating the entire process chain for dating of alpine glacier ice by argon trap trace analysis (ArTTA). Ice blocks as small as a few kilograms are sufficient and have been obtained at two artificial glacier caves. Importantly, both sites offer direct access to the stratigraphy at the glacier base and validation against existing age constraints. The ice blocks obtained at Chli Titlis glacier at 3,030 m asl (Swiss Alps) have been dated by state-of-the-art microradiocarbon analysis in a previous study. The unique finding of a bark fragment and a larch needle within the ice of Schaufelferner glacier at 2,870 m asl (Stubai Alps, Austria) allows for conventional radiocarbon dating. At both sites the existing age information based on radiocarbon dating and visual stratigraphy corroborates the 39Ar ages. With our results, we establish argon trap trace analysis as the key to decipher so far untapped glacier archives of the last millennium.