MASSIVE compact objects in the Galactic halo, known as MACHOs, have been postulated as the origin of a substantial fraction of the ’dark matter’ known to exist in the haloes of galaxies(1,2). Paczynski(3) has suggested that it might be possible to detect these low-luminosity objects by their potential to act as gravitational lenses, causing a characteristic brightening when they cross the path of light from a star in a nearby galaxy. Very recently, two groups reported possible detections of microlensing of stars in the Large Magellanic Cloud (LMC)(4,5), which was interpreted as a possible fingerprint of MACHOs. Here I show that microlensing by stars within the LMC itself can account for the observed events. In the future it should be possible to distinguish between the two possible sources of microlensing events, however, because events caused by stars in the LMC should be clustered toward the central region of that galaxy,whereas those caused by MACHOs should be uniformly distributed over the whole LMC.