  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.
