The solar neighbourhood is the closest and most easily studied sample of the Galactic interstellar medium, an understanding of which is essential for models of star formation and galaxy evolution. Observations of an unexpectedly intense diffuse flux of easily absorbed 1/4-kiloelectronvolt X-rays, coupled with the discovery that interstellar space within about a hundred parsecs of the Sun is almost completely devoid of cool absorbing gas, led to a picture of a 'local cavity' filled with X-ray-emitting hot gas, dubbed the local hot bubble. This model was recently challenged by suggestions that the emission could instead be readily produced within the Solar System by heavy solar-wind ions exchanging electrons with neutral H and He in interplanetary space, potentially removing the major piece of evidence for the local existence of million-degree gas within the Galactic disk. Here we report observations showing that the total solar-wind charge-exchange contribution is approximately 40 per cent of the 1/4-keV flux in the Galactic plane. The fact that the measured flux is not dominated by charge exchange supports the notion of a million-degree hot bubble extending about a hundred parsecs from the Sun.