We study a model in which dark matter couples to the Standard Model through a dilaton of a sector with spontaneously broken approximate scale invariance. Scale invariance fixes the dilaton couplings to the Standard Model and dark matter fields, leaving three main free parameters: the symmetry breaking scale f, the dilaton mass m(sigma), and the dark matter mass m(chi). We analyze the experimental constraints on the parameter space from collider, direct and indirect detection experiments including the effect of Sommerfeld enhancement, and show that dilaton exchange provides a consistent, calculable framework for cold dark matter with f, ma, mx of roughly similar magnitude and in the range 1-10 TeV. Direct and indirect detection experiments, notably future ground-based gamma ray and space-based cosmic ray measurements, can probe the model all the way to dark matter mass in the multi-TeV regime.