Radiocarbon ((14)C) concentrations at a 43 parts-per-quadrillion level are measured by using saturated-absorption cavity ringdown spectroscopy by exciting radiocarbon-dioxide ((14)C(16)O(2)) molecules at the 4.5 μm wavelength. The ultimate sensitivity limits of molecular trace gas sensing are pushed down to attobar pressures using a comb-assisted absorption spectroscopy setup. Such a result represents the lowest pressure ever detected for a gas of simple molecules. The unique sensitivity, the wide dynamic range, the compactness, and the relatively low cost of this table-top setup open new perspectives for ^{14}C-tracing applications, such as radiocarbon dating, biomedicine, or environmental and earth sciences. The detection of other very rare molecules can be pursued as well thanks to the wide and continuous mid-IR spectral coverage of the described setup.