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Following our previous detection of ubiquitous H₂O and O₂ absorption against the far-ultraviolet continuum of stars located near the nucleus of Comet 67P/Churyumov-Gerasimenko, we present a serendipitously observed stellar occultation that occurred on 2015 September 13, approximately one month after the comet's perihelion passage. The occultation appears in two consecutive 10-minute spectral images obtained by Alice, Rosetta's ultraviolet (700-2100 Å) spectrograph, both of which show H₂O absorption with column density >10^17.5 cm^–2 and significant O₂ absorption (O₂/H₂O ≃ 5%-10%). Because the projected distance from the star to the nucleus changes between exposures, our ability to study the H₂O column density profile near the nucleus (impact parameters <1 km) is unmatched by our previous observations. We find that the H₂O and O₂ column densities decrease with increasing impact parameter, in accordance with expectations, but the O₂ column decreases ∼3 times more quickly than H₂O. When combined with previously published results from stellar appulses, we conclude that the O₂ and H₂O column densities are highly correlated, and O₂/H₂O decreases with the increasing H₂O column.