Knowledge about the outermost portions of galaxies is limited owing to the small amount of light coming from them. It is known that in many cases atomic hydrogen (H I) extends well beyond the optical radius 1 . In the centres of galaxies, however, molecular hydrogen (H 2 ) usually dominates by a large factor [2][3][4] , raising the question of whether H 2 is also abundant in the outer regions. Here we report the detection of emission from carbon monoxide (CO), the most abundant tracer of H 2 , beyond the optical radius of the nearby galaxy NGC 4414. The host molecular clouds probably formed in the regions of relatively high H I column density and in the absence of spiral density waves. The relative strength of the lines from the two lowest rotational levels indicates that both the temperature and density of the H 2 are quite low compared to conditions closer to the centre. The inferred surface density of the molecular material continues the monotonic decrease from the inner regions. We conclude that although molecular clouds can form in the outer region of this galaxy, there is little mass associated with them.The CO spectra shown in Fig. 1 reveal the presence of cool, but not very cold, molecular gas out to 1.5 times the optical radius (R 25 ) of the isolated spiral NGC 4414. The CO observations were carried out in good conditions with the 30-m antenna on Pico Veleta (Spain) operated by the Institut de Radioastronomie Millimétrique, in May and November 2003, and March 2004. Cool H 2 is not directly observable because it has no permitted rotational transitions so CO, the most abundant heteronuclear molecular, is used as a proxy. The galaxy chosen is expected to be representative of a large class of spirals because it is of late type, quite axisymmetric 5 , and has no immediate neighbours with which it could interact. The atomic gas is extended, also indicating a lack of major interactions. This lack of interactions is important: although every interaction is different owing to the large number of parameters involved, isolated galaxies can reasonably be hoped to be representative. Furthermore, NGC 4414 is near the North Galactic Pole and suffers little from foreground (Galactic) confusion or extinction.Almost no constraints are as yet available on the H 2 content of the outer disks of spirals. To our knowledge, these are the first published detections of CO beyond the optical radius of an external spiral, reaching 1.5R 25 . A. Ferguson also reports detection (personal communication) of CO in NGC 6946 beyond R 25 . Digel et al. 6 detected isolated clouds at large radii in the Milky Way, although the mass implied was quite low. Our previously published observations of NGC 4414, covering almost the whole optical disk, show a clear decline in the CO(2 2 1)/CO(1 2 0) line ratio (independent of beam size) which we interpret 7 as a decrease in excitation temperature, meaning that even if substantial CO is present, the lines could be quite weak. Dust, which is necessary for H 2 formation, is clearly seen in absorption at...