Thermal management is one of the main challenges for the future of electronics(1-5). With the ever-increasing rate of data generation and communication, as well as the constant push to reduce the size and costs of industrial converter systems, the power density of electronics has risen(6). Consequently, cooling, with its enormous energy and water consumption, has an increasingly large environmental impact(7,8), and new technologies are needed to extract the heat in a more sustainable way-that is, requiring less water and energy(9). Embedding liquid cooling directly inside the chip is a promising approach for more efficient thermal management(5,10,11). However, even in state-of-the-art approaches, the electronics and cooling are treated separately, leaving the full energy-saving potential of embedded cooling untapped. Here we show that by co-designing microfluidics and electronics within the same semiconductor substrate we can produce a monolithically integrated manifold microchannel cooling structure with efficiency beyond what is currently available. Our results show that heat fluxes exceeding 1.7 kilowatts per square centimetre can be extracted using only 0.57 watts per square centimetre of pumping power. We observed an unprecedented coefficient of performance (exceeding 10,000) for single-phase water-cooling of heat fluxes exceeding 1 kilowatt per square centimetre, corresponding to a 50-fold increase compared to straight microchannels, as well as a very high average Nusselt number of 16. The proposed cooling technology should enable further miniaturization of electronics, potentially extending Moore's law and greatly reducing the energy consumption in cooling of electronics. Furthermore, by removing the need for large external heat sinks, this approach should enable the realization of very compact power converters integrated on a single chip.