The evolution of infinitesimal three-dimensional perturbations superimposed on a Burgers vortex is studied. By a sequence of variable transformations and scalings this linear evolution problem is reduced to a time-dependent system which is nearly identical to the stability equations governing a Lamb–Oseen vortex. The maximum amplification reached by perturbations over a finite time interval is computed through an iterative scheme based on the direct and adjoint governing equations, and results on the asymptotic stability of the Burgers vortex are deduced. The Burgers vortex is shown to be asymptotically stable, although significant short-term amplification may occur.