By compressing elemental silicon and hydrogen in a diamond anvil cell, we have synthesized polymeric silicon tetrahydride (SiH(4)) at 124 GPa and 300 K. In situ synchrotron x-ray diffraction reveals that the compound forms the insulating I4(1)/a structure previously proposed from ab initio calculations for the high-pressure phase of silane. From a series of high-pressure experiments at room and low temperature on silane itself, we find that its tetrahedral molecules break up, while silane undergoes pressure-induced amorphization at pressures above 60 GPa, recrystallizing at 90 GPa into the polymeric crystal structures.