  We present the results of deep optical spectroscopic observations using the
LRIS spectrograph on the Keck I 10-m telescope of three ultra-luminous X-ray
sources (ULXs), Ho IX X-1; M81 X-6; and Ho II X-1. Our observations reveal the
existence of large (100 - 200 pc diameter) highly-ionized nebulae, identified
by diffuse He II (4686 Angstrom) emission, surrounding these sources. Our
results are the first to find highly-ionized nebulae of this extent, and the
detection in all three objects indicates this may be a common feature of ULXs.
In addition to the extended emission, Ho IX X-1 has an unresolved central
component containing about one-third of the total He II flux, with a
significant velocity dispersion of ~ 370 km/s, suggestive of the existence of a
photo-ionized accretion disk or an extremely hot early-type stellar
counterpart. Most of the He II emission appears to be surrounded by
significantly more extended Hbeta emission, and the intensity ratios between
the two lines, which range from 0.12 - 0.33, indicate that photo-ionization is
the origin of the He II emission. Sustaining these extended nebulae requires
substantial X-ray emission, in the range ~ 10^{39} - 10^{40} ergs/s, comparable
to the measured X-ray luminosities of the sources. This favors models where the
X-ray emission is isotropic, rather than beamed, which includes the
interpretation that ULXs harbor intermediate-mass black holes.
