Random numbers are a fundamental resource in science and technology. Among the different approaches to generating them, random numbers created by exploiting the laws of quantum mechanics have proven to be reliable and can be produced at enough rates for their practical use. While these demonstrations have shown very good performance, most of the implementations using free-space and fibre optics suffer from limitations due to their size, which strongly limits their practical use. Here we report a quantum random number generator based on phase fluctuations from a diode laser, where the other required optical components are integrated on a mm-scale monolithic silicon-on-insulator chip. The post-processing reported in this experiment is performed via software. However, our physical device shows the potential of operation at generation rates in the Gbps regime. Considering the device's size, its simple, robust and low power operation, and the rapid industrial uptake of silicon photonics, we foresee the widespread integration of the reported design in more complex systems.