  Studies of young stellar objects (YSOs) in the Galaxy have found that a
significant fraction exhibit photometric variability. However, no systematic
investigation has been conducted on the variability of extragalactic YSOs. Here
we present the first variability study of massive YSOs in a $\sim
1.5\,\mathrm{deg^2}$ region of the Large Magellanic Cloud (LMC). The aim is to
investigate whether the different environmental conditions in the metal-poor
LMC ($\sim$ 0.4-0.5 Z_sun) have an impact on the variability characteristics.
Multi-epoch near-infrared (NIR) photometry was obtained from the VISTA Survey
of the Magellanic Clouds (VMC) and our own monitoring campaign using the VISTA
telescope. By applying a reduced $\chi^2$-analysis, stellar variability was
identified. We found 3062 candidate variable stars from a population of 362 425
stars detected. Based on several Spitzer studies, we compiled a sample of
high-reliability massive YSOs: a total of 173 massive YSOs have NIR
counterparts ($K_{\mathrm{s}}\sim 18.5\,$mag) in the VMC catalogue, of which 39
display significant ($>3\sigma$) variability. They have been classified as
eruptive, fader, dipper, short-term variable and long-period variable YSOs
based mostly on the appearance of their $K_{\mathrm{s}}$ band light curves. The
majority of YSOs are aperiodic, only five YSOs exhibit periodic lightcurves.
The observed amplitudes are comparable or smaller than those for Galactic YSOs
(only two Magellanic YSOs exhibit $\Delta K_{\mathrm{s}}>1\,$mag), not what
would have been expected from the typically larger mass accretion rates
observed in the Magellanic Clouds.
