Transient control over the atomic potential-energy landscapes of solids could lead to new states of matter and to quantum control of nuclear motion on the timescale of lattice vibrations. Recently developed ultrafast time-resolved diffraction techniques(1) combine ultrafast temporal manipulation with atomic-scale spatial resolution and femtosecond temporal resolution. These advances have enabled investigations of photo-induced structural changes in bulk solids that often occur on timescales as short as a few hundred femtoseconds(2-6). In contrast, experiments at surfaces and on single atomic layers such as graphene report timescales of structural changes that are orders of magnitude longer(7-9). This raises the question of whether the structural response of low-dimensional materials to femtosecond laser excitation is, in general, limited. Here we show that a photo-induced transition from the low-to high-symmetry state of a charge density wave in atomic indium (In) wires supported by a silicon (Si) surface takes place within 350 femtoseconds. The optical excitation breaks and creates In-In bonds, leading to the non-thermal excitation of soft phonon modes, and drives the structural transition in the limit of critically damped nuclear motion through coupling of these soft phonon modes to a manifold of surface and interface phonons that arise from the symmetry breaking at the silicon surface. This finding demonstrates that carefully tuned electronic excitations can create non-equilibrium potential energy surfaces that drive structural dynamics at interfaces in the quantum limit (that is, in a regime in which the nuclear motion is directed and deterministic)(8). This technique could potentially be used to tune the dynamic response of a solid to optical excitation, and has widespread potential application, for example in ultrafast detectors(10,11).