The Solar neighborhood 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 keV X rays, coupled with the discovery that interstellar space within ~100 pc 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 upset by suggestions that the emission could instead be produced readily within the solar system by heavy solar wind ions charge exchanging with neutral H and He in interplanetary space, potentially removing the major piece of evidence for the existence of million-degree gas within the Galactic disk. Here we report results showing that the total solar wind charge exchange contribution is 40% +/- 5% (stat) +/- 5% (sys) 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 of order 100 pc extent surrounding the Sun.