PIE base ‘whole, uninjured, of good omen’. See also sol-, root of holism, catholic, and safe.
It seems to be a happy coincidence that the PIE base for health, holy, and whole, through Old High German and Old English, should have a quite different PIE base from all the holo- words, via Greek.
[Pokorny *kai-lo- (kai-lu-), p. 520, ‘bright; safe, hale, healthy’.]