Abstract The neutral atomic gas content of individual galaxies at large cosmological distances has until recently been difficult to measure due to the weakness of the hyperfine H i 21 cm transition. Here we estimate the H i gas mass of a sample of main-sequence star-forming galaxies at z ∼ 6.5–7.8 surveyed for C ii 158 μ m emission as part of the Reionization Era Bright Emission Line Survey (REBELS), using a recent calibration of the C ii -to-H i conversion factor. We find that the H i gas mass excess in galaxies increases as a function of redshift, with an average of M H i / M ⋆ ≈ 10, corresponding to H i gas mass fractions of f H i = M H i /( M ⋆ + M H i ) = 90%, at z ≈ 7. Based on the C ii 158 μ m luminosity function (LF) derived from the same sample of galaxies, we further place constraints on the cosmic H i gas mass density in galaxies ( ρ H i ) at this redshift, which we measure to be ρ H I = 7.1 − 3.0 + 6.4 × 10 6 M ⊙ Mpc − 3 . This estimate is substantially lower by a factor of ≈10 than that inferred from an extrapolation of damped Ly α absorber (DLA) measurements and largely depends on the exact C ii LF adopted. However, we find this decrease in ρ H i to be consistent with recent simulations and argue that this apparent discrepancy is likely a consequence of the DLA sight lines predominantly probing the substantial fraction of H i gas in high- z galactic halos, whereas C ii traces the H i in the ISM associated with star formation. We make predictions for this buildup of neutral gas in galaxies as a function of redshift, showing that at z ≳ 5, only ≈10% of the cosmic H i gas content is confined in galaxies and associated with the star-forming ISM.