Phase-locked ultrashort pulses in the rich terahertz spectral range(1-18) have provided key insights into phenomena as diverse as quantum confinement(7), first-order phase transitions(8,12), high-temperature superconductivity(11) and carrier transport in nanomaterials(1,6),(13-15). Ultrabroadband electrooptic sampling of few-cycle field transients(1) can even reveal novel dynamics that occur faster than a single oscillation cycle of light(4,8,10). However, conventional terahertz spectroscopy is intrinsically restricted to ensemble measurements by the diffraction limit. As a result, it measures dielectric functions averaged over the size, structure, orientation and density of nanoparticles, nanocrystals or nanodomains. Here, we extend ultrabroadband time-resolved terahertz spectroscopy to the sub-nanoparticle scale (10 nm) by combining subcycle, field-resolved detection (10 fs) with scattering-type near-field scanning optical microscopy (s-NSOM)(16-26). We trace the time-dependent dielectric function at the surface of a single photoexcited InAs nanowire in all three spatial dimensions and reveal the ultrafast (<50 fs) formation of a local carrier depletion layer.