In the era of precision cosmology, it is essential to determine the Hubble constant empirically with an accuracy of one per cent or better(1). At present, the uncertainty on this constant is dominated by the uncertainty in the calibration of the Cepheid period-luminosity relationship(2,3) (also known as the Leavitt law). The Large Magellanic Cloud has traditionally served as the best galaxy with which to calibrate Cepheid period-luminosity relations, and as a result has become the best anchor point for the cosmic distance scale(4,5). Eclipsing binary systems composed of late-type stars offer the most precise and accurate way to measure the distance to the Large Magellanic Cloud. Currently the limit of the precision attainable with this technique is about two per cent, and is set by the precision of the existing calibrations of the surface brightness-colour relation(5,6). Here we report a calibration of the surface brightness-colour relation with a precision of 0.8 per cent. We use this calibration to determine a geometrical distance to the Large Magellanic Cloud that is precise to 1 per cent based on 20 eclipsing binary systems. The final distance is 49.59 +/- 0.09 (statistical) +/- 0.54 (systematic) kiloparsecs.