Carbon-14 (14C) is incorporated into glacial ice by trapping of atmospheric gases as well as direct near-surface in situ cosmogenic production. 14C of trapped methane (14CH4) is a powerful tracer for past CH4 emissions from “old” carbon sources such as permafrost and marine CH4 clathrates. 14C in trapped carbon dioxide (14CO2) can be used for absolute dating of ice cores. In situ produced cosmogenic 14C in carbon monoxide (14CO) can potentially be used to reconstruct the past cosmic ray flux and past solar activity. Unfortunately, the trapped atmospheric and in situ cosmogenic components of 14C in glacial ice are difficult to disentangle and a thorough understanding of the in situ cosmogenic component is needed in order to extract useful information from ice core 14C. We analyzed very large (≈1000 kg) ice samples in the 2.26–19.53 m depth range from the ablation zone of Taylor Glacier, Antarctica, to study in situ cosmogenic production of 14CH4 and 14CO. All sampled ice is >50 ka in age, allowing for the assumption that most of the measured 14C originates from recent in situ cosmogenic production as ancient ice is brought to the surface via ablation. Our results place the first constraints on cosmogenic 14CH4 production rates and improve on prior estimates of 14CO production rates in ice. We find a constant 14CH4/14CO production ratio (0.0076 ± 0.0003) for samples deeper than 3 m, which allows the use of 14CO for correcting the 14CH4 signals for the in situ cosmogenic component. Our results also provide the first unambiguous confirmation of 14C production by fast muons in a natural setting (ice or rock) and suggest that the 14C production rates in ice commonly used in the literature may be too high.