  We report results from a neutral hydrogen (HI) intensity mapping survey
conducted with a Phased Array Feed (PAF) on the Parkes telescope. The survey
was designed to cover ~ 380 deg^2 over the redshift range 0.3 < z < 1 (a volume
of ~ 1.5 Gpc^3) in four fields covered by the WiggleZ Dark Energy Survey. The
results presented here target a narrow redshift range of 0.73 < z < 0.78 where
the effect of radio frequency interference (RFI) was less problematic. The data
reduction and simulation pipeline is described, with an emphasis on flagging of
RFI and correction for signal loss in the data reduction process, particularly
due to the foreground subtraction methodology. A cross-correlation signal was
detected between the HI intensity maps and the WiggleZ redshift data, with a
mean amplitude of<{\Delta}T_b{\delta}_{opt}> = 1.32 \pm 0.42 mK (statistical
errors only). A future Parkes cryogenic PAF is expected to detect the
cross-correlation signal with higher accuracy than previously possible and
allow measurement of the cosmic HI density at redshifts up to unity.
