We estimate the momentum diffusion coefficient of a heavy quark within a pure SU(3) plasma at a temperature of about 1.5T c . Large-scale Monte Carlo simulations on a series of lattices extending up to 192 3 × 48 permit us to carry out a continuum extrapolation of the so-called colour-electric imaginary-time correlator. The extrapolated correlator is analyzed with the help of theoretically motivated models for the corresponding spectral function. Evidence for a non-zero transport coefficient is found and, incorporating systematic uncertainties reflecting model assumptions, we obtain κ = (1.8 − 3.4) T 3 . This implies that the "drag coefficient", characterizing the time scale at which heavy quarks adjust to hydrodynamic flow, is η −1 D = (1.8 − 3.4)(T c /T ) 2 (M/1.5GeV) fm/c, where M is the heavy quark kinetic mass. The results apply to bottom and, with somewhat larger systematic uncertainties, to charm quarks.