  We present HST spectroscopy and imaging, along with new ground-based
spectroscopy and ROSAT HRI imaging, of the He II emitting nebula N44C and its
ionizing star. A GHRS spectrogram of the ionizing star yields a spectral type
of about O7 for the star. The lack of P Cygni profiles for Si IV and C IV
indicates that the star is not a supergiant. The nebular abundances in the
ionized gas are consistent with average abundances for LMC H II regions, with
the possible exception that nitrogen may be enhanced. Enrichment by a former
evolved companion star is not evident. A long-slit echelle spectrogram in
H-alpha + [N II] shows no evidence for high-velocity gas in N44C. This rules
out high-velocity shocks as the source of the nebular He II emission. A 108 ks
ROSAT HRI image of N44C shows no X-ray point source to a 3-sigma upper limit
L(X) < 10^34 erg s^-1 in the 0.1-2.0 keV band. Based on new measurements of the
electron density in the He II emitting region, we derive recombination
timescales of approximately 20 yrs for He^+2 and approximately 4 yrs for Ne^+4.
If N44C is a fossil X-ray ionized nebula, this places severe constraints on
when the putative X-ray source could have turned off. The presence of strong
[Ne IV] emission in the nebula is puzzling if the ionizing source has turned
off. It is possible the system is related to the Be X-ray binaries, although
the O star in N44C does not show Be characteristics at the present time.
Monitoring of X-rays and He II emission from the nebula, as well as a radial
velocity study of the ionizing star, are needed to fully understand the
emission line spectrum of N44C.
