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 μm and [C ii] 158 μm. CO(6−5), CO(7−6), and [C i](2−1), whose 3σ 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) × 10¹⁰ 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.