The thermoelectric power of the two-dimensional electron system (2DES) at the LaAlO3/SrTiO3 interface is explored below room temperature, in comparison with that of Nb-doped SrTiO3 single crystals. For the interface, we find a region below T=50 K where thermopower is dominated by phonon drag, whose amplitude is hugely amplified with respect to the corresponding bulk value, reaching values ∼mV/K and above. The phonon-drag enhancement at the interface is traced back to the tight carrier confinement of the 2DES, and represents a sharp signature of strong electron-acoustic phonon coupling at the interface.