We present results of accurate Variational Monte Carlo simulations of
a f.c.c. He-4 crystal with a vacancy at T = 0. Calculations are based
on the Shadow Wave Function sheme, in which the vacancy can move throu
gh the crystal and no a priori equilibrium positions for the atoms are
assumed. This is the first microscopic calculation g iving a realisti
c value for the energy of a vacancy, in the range 15-38 K depending on
the density of the solid. Results on the mobility of the vacancy are
presented.