We study different solid phases of Helium-four, by means of Path Integral Monte Carlo simulations based on a recently developed {\it worm} algorithm. Our study includes simulations that start off from a high-T disordered phase (at the T=0 melting density of the hcp crystal) which is then "quenched". The low-T properties of the system crucially depend on the initial state. While an ideal hcp crystal is a clear-cut insulator, the disordered system quenched down to T=0.2 K freezes into a superglass, namely a metastable amorphous solid phase, that features off-diagonal long-range order and superfluidity.