  We explore X-ray emission from a sample of 18 He II 1640 emitting
star-forming galaxies at z ~ 2.3-3.6 from the VANDELS survey in the Chandra
Deep Field South, to set constraints on the role of X-ray sources in powering
the He II emission. We find that 4 He II emitters have tentative detections
with S/N ~ 2 and have X-ray luminosities, L_X = 1.5-4.9 x 10^41 erg/s. The
stacked luminosity of all 18 He II emitters is 2.6 x 10^41 erg/s, and that of a
subset of 13 narrow He II emitters (FHWM(He II) < 1000 km/s) is 3.1 x 10^41
erg/s. We also measure stacked L_X for non-He II emitters through bootstrapping
of matched samples, and find L_X = 2.5 x 10^41 erg/s, which is not
significantly different from L_X measured for He II emitters. The L_X per
star-formation rate for He II emitters (log (L_X/SFR) ~ 40.0) and non-emitters
(log (L_X/SFR) ~ 39.9) are also comparable and in line with the redshift
evolution and metallicity dependence predicted by models. Due to the
non-significant difference between the X-ray emission from galaxies with and
without He II, we conclude that X-ray binaries or weak or obscured AGNs are
unlikely to be the dominant producers of He II ionising photons in VANDELS
star-forming galaxies at z ~ 3. Given the comparable physical properties of
both He II emitters and non-emitters reported previously, alternative He II
ionising mechanisms such as localised low-metallicity stellar populations,
Pop-III stars, etc. may need to be explored.
