The continuous scaling of semiconductor-based technologies to micron and sub-micron regimes has resulted in higher device density and lower power dissipation. Many physical phenomena such as self-heating or current leakage become significant at such scales, and mapping current densities to reveal these features is decisive for the development of modern electronics. However, advanced non-invasive technologies either offer low sensitivity or poor spatial resolution and are limited to two-dimensional spatial mapping. Here we use shallow nitrogen-vacancy centres in diamond to probe Oersted fields created by current flowing within a multi-layered integrated circuit in pre-development. We show the reconstruction of the three-dimensional components of the current density with a magnitude down to and sub-micron spatial resolution capabilities at room temperature. We also report the localisation of currents in different layers and observe anomalous current flow in an electronic chip. Further improvements using decoupling sequences and material optimisation will lead to nA-current detection at sub-micron spatial resolution. Our method provides therefore a decisive breakthrough towards three-dimensional current mapping in technologically relevant nanoscale electronics chips.