Optical fibre communication is the backbone of the internet. As essential core technologies are approaching their limits of size, speed and energy-efficiency, there is a need for new technologies that offer further scaling of data transmission capacity. Here we show that a single optical frequency-comb source based on a silicon nitride ring resonator supports data capacities in the petabit-per-second regime. We experimentally demonstrate transmission of 1.84 Pbit s–1 over a 37-core, 7.9-km-long fibre using 223 wavelength channels derived from a single microcomb ring resonator producing a stabilized dark-pulse Kerr frequency comb. We also present a theoretical analysis that indicates that a single, chip-scale light source should be able to support 100 Pbit s–1 in massively parallel space-and-wavelength multiplexed data transmission systems. Our findings could mark a shift in the design of future communication systems, targeting device-efficient transmitters and receivers. A microcomb source based on a silicon nitride ring resonator is shown to support petabit-per-second data transmission over a multicore optical fibre.