Entanglement, an essential feature of quantum theory that allows for inseparable quantum correlations to be shared between distant parties, is a crucial resource for quantum networks(1). Of particular importance is the ability to distribute entanglement between remote objects that can also serve as quantum memories. This has been previously realized using systems such as warm(2,3) and cold atomic vapours(4,5), individual atoms(6) and ions(7,8), and defects in solid-state systems(9-11). Practical communication applications require a combination of several advantageous features, such as a particular operating wavelength, high bandwidth and long memory lifetimes. Here we introduce a purely micromachined solid-state platform in the form of chip-based optomechanical resonators made of nanostructured silicon beams. We create and demonstrate entanglement between two micromechanical oscillators across two chips that are separated by 20 centimetres. The entangled quantum state is distributed by an optical field at a designed wavelength near 1,550 nanometres. Therefore, our system can be directly incorporated in a realistic fibre-optic quantum network operating in the conventional optical telecommunication band. Our results are an important step towards the development of large-area quantum networks based on silicon photonics.