Matter-wave interferometry performed with massive objects elucidates their wave nature and thus tests the quantum superposition principle at large scales. Whereas standard quantum theory places no limit on particle size, alternative, yet untested theories can be conceived which forbid macroscopic superpositions. Here we propose an interferometer with a levitated, optically cooled, and then free-falling silicon nanoparticle in the mass range of one million atomic mass units delocalized over more than 150 nm. The scheme employs the near-field Talbot effect with a single standing-wave laser pulse as a phase grating. Our analysis, which accounts for all relevant sources of decoherence, indicates that this is a viable route towards macroscopic high-mass superpositions using available technology.