High power laser delivery with near-diffraction-limited beam quality, widely used in industry for precision manufacturing, is typically limited to tens of metres distances by nonlinearity-induced spectral broadening inside the glass-core delivery fibres. Anti-resonant hollow-core fibres offer not only orders-of-magnitude lower non-linearity, but also loss and modal purity comparable to conventional beam-delivery fibres. Using a single-mode hollow-core nested anti-resonant nodeless fibre (NANF) with 0.74-dB/km loss, we demonstrate delivery of 1 kW of near-diffraction-limited continuous wave laser light over an unprecedented 1-km distance, with a total throughput efficiency of ~80%. From simulations, more than one order of magnitude further improvement in transmitted power or length should be possible in such air-filled fibres, and considerably more if the core is evacuated. This paves the way to multi-kilometre, kW-scale power delivery – not only for future manufacturing and subsurface drilling, but also for new scientific possibilities in sensing, particle acceleration and gravitational wave detection.