An excess of far-infrared emission is seen towards the nearby G8V star τ Ceti, and this has been attributed to orbiting dust particles generated in planetesimal collisions. A new 850-μm image shows that there is indeed such a debris disc, extending out to ~55 au (15 arcsec) radius. This is the first disc around a Sun-like star of late main-sequence age to be confirmed by imaging. The dust mass is at least an order of magnitude greater than in the Kuiper Belt, although the dimensions of the systems are very similar and the age of τ Ceti exceeds that of the Sun. Modelling shows that the mass in colliding bodies up to 10 km in size is around 1.2 Earth masses, compared with 0.1 M⊕ in the Kuiper Belt, and hence the evolution around the two stars has been different. One possibility is that τ Ceti has lost fewer comets from the outskirts of the system, compared with the Sun. Alternatively, a greater number of comets could have been forced out by a migrating planet, compared with the case of Neptune in the Solar system. Notably, the disc of τ Ceti fits the expected decline with time compared to that of the younger nearby star ∊ Eridani. Among these three stars, the Sun would then be the case with the least dust and a `minimal Kuiper Belt' - a situation which may be beneficial in terms of less bombardment and better stability for life.