We propose a novel, local Hall-probe magnetometry technique for the investigation of magnetic phenomena in superconductors. A miniaturized (80 x 100-mu-m2 size) Hall sensor allows us to measure magnetic features with a precision approaching that of a single vortex line. We demonstrate the efficiency of this technique by exhibiting magnetic data for YBa2Cu3O7 single crystals. These include magnetization curves, and determination of H*, the first field for full penetration.