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We report Atacama Large Millimeter/submillimeter Array Band 3 observations of CO(6−5), CO(7−6), and [C i ](2−1) in B14-65666 (“Big Three Dragons”), one of the brightest Lyman-break galaxies at z > 7 in the rest-frame ultraviolet continuum, far-infrared continuum, and emission lines of [O iii ] 88 μ m and [C ii ] 158 μ m. CO(6−5), CO(7−6), and [C i ](2−1), whose 3 σ upper limits on the luminosities are approximately 40 times fainter than the [C ii ] luminosity, are all not detected. The L _[C _II _] / L _CO(6–5) and L _[C _II _] / L _CO(7–6) ratios are higher than the typical ratios obtained in dusty star-forming galaxies or quasar host galaxies at similar redshifts, and they may suggest a lower gas density in the photodissociated region in B14-65666. By using the (1) [C ii ] luminosity, (2) dust mass-to-gas mass ratio, and (3) a dynamical mass estimate, we find that the molecular gas mass ( M _mol ) is (0.05–11) × 10 ^10 M _⊙ . This value is consistent with the upper limit inferred from the nondetection of mid- J CO and [C i ](2−1). Despite the large uncertainty in M _mol , we estimate a molecular gas-to-stellar mass ratio ( μ _gas ) of 0.65–140 and a gas depletion time ( τ _dep ) of 2.5–550 Myr; these values are broadly consistent with those of other high-redshift galaxies. B14-65666 could be an ancestor of a passive galaxy at z ≳ 4 if no gas is fueled from outside the galaxy.