The large-scale distribution of neutral hydrogen in the Universe will be luminous through its 21 cm emission. Here, for the first time, we use the auto-power spectrum of 21 cm intensity fluctuations to constrain neutral hydrogen fluctuations at z~0.8. Our data were acquired with the Green Bank Telescope and span the redshift range 0.6 < z < 1 over two fields totalling ~41 deg. sq. and 190 h of radio integration time. The dominant synchrotron foregrounds exceed the signal by ~10^3, but have fewer degrees of freedom and can be removed efficiently. Even in the presence of residual foregrounds, the auto-power can still be interpreted as an upper bound on the 21 cm signal. Our previous measurements of the cross-correlation of 21 cm intensity and the WiggleZ galaxy survey provide a lower bound. Through a Bayesian treatment of signal and foregrounds, we can combine both fields in auto- and cross-power into a measurement of Omega_HI b_HI = [0.62^{+0.23}_{-0.15}] * 10^{-3} at 68% confidence with 9% systematic calibration uncertainty, where Omega_HI is the neutral hydrogen (HI) fraction and b_HI is the HI bias parameter. We describe observational challenges with the present data set and plans to overcome them.
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