Sodium chloride (NaCl), or rocksalt, is well characterized at ambient pressure. As a result of the large electronegativity difference between Na and Cl atoms, it has highly ionic chemical bonding (with 1:1 stoichiometry dictated by charge balance) and B1-type crystal structure. By combining theoretical predictions and diamond anvil cell experiments, we found that new materials with different stoichiometries emerge at high pressures. Compounds such as Na3Cl, Na2Cl, Na3Cl2, NaCl3, and NaCl7 are theoretically stable and have unusual bonding and electronic properties. To test this prediction, we synthesized cubic and orthorhombic NaCl3 and two-dimensional metallic tetragonal Na3Cl. These experiments establish that compounds violating chemical intuition can be thermodynamically stable even in simple systems at nonambient conditions.