A sequence of pressure-induced phase transitions of vaesite, NiS(2), with pyrite structure, has been established from static LDA calculations. A dozen AX(2) candidate structures have been studied at high pressures including cotunnite (α-PbCl(2)), which is commonly observed in other AX(2) compounds at high pressures. At 150 GPa, vaesite transforms to a tetragonal phase (P4(2)/n) rather than cotunnite. This tetragonal structure is characterized by layers of Ni atoms in eight-fold coordination with S atoms rather than the nine-fold coordination observed in cotunnite. With further compression to about 7.5 Mbar, the tetragonal phase transforms into a hexagonal AlB(2)-type structure (P6/mmm) which is characterized by planar hexagonal layers of S intercalated by Ni atoms where each Ni atom is 12-fold coordinated by S atoms. Calculated band structures and valence electron density maps show S-S and Ni-S bonded interactions for NiS(2) under these extremely compressed conditions. The tetragonal phase may have geophysical implications if present in the Earth's core.