The sign of the interference (constructive or destructive) between quantum-mechanical paths depends on the phase difference between the paths, In the Fano effect(1) two optical paths from the ground state of a system-one direct and one mediated by a resonance-to a state in an energy continuum interfere to produce an asymmetric absorption spectrum that falls to zero near the absorption maximum. Zero absorption occurs as the wavelength is scanned across the resonance, at a photon energy corresponding to a 180 degrees phase difference between the paths, Similar interference effects occur when two absorption paths are mediated by two different states, and they provide the basis for lasers that operate without a population inversion(2-7). Here we report the control, by quantum mechanical tunnelling, of interference in optical absorption. The two intermediate states are resonances that arise from the mixing of the states in two adjacent semiconductors quantum wells, which are broadened by tunnelling into the same energy continuum through an ultra-thin potential-energy barrier, Inverting the direction of tunnelling by reversing the position of the barrier with respect to the two quantum wells changes the interference from destructive to constructive, as predicted theoretically, This effect might provide a way to make semiconductor lasers without population inversions(8).