We describe the zero-temperature crystallization of superfluid He-4 within a Ramakrishnan-Yussouff approach, exploiting a recent extension of density functional formalism to treat the freezing of quantum liquids. This is the first zero-temperature application to a real system. In particular, we discuss i) the importance of the static response function of the homogeneous fluid in determining the transition, and ii) the quantitative effects of overlap, as can be inferred from the large value of Lindemann ratio for quantum freezing.