Seems nobody likes my answer, even though it's right. Oh well... Please delete this!

While diamonds are one of the most popular and command a high price for quality stones, there is another gemstone that surpasses the diamond in cost and rarity. It is Alexandrite. One of Earth's most rare and spectacular gemstones, Alexandrite is rightfully called "The Most Expensive Gemstone in The World." Alexandrite has the ability to change its color, going from a rich blue while in sunlight to a vibrant rasberry when placed in incadescent light. Discovered in Russia in the Ural mountains in 1830, it was named after Czar Alexander the Second. Alexandrite's colors match the national colors of Russia. It is a form of chrysoberyl, beryllium aluminate, with chromium and/or vanadium as an impurity. This chromium inpurity can produce the red in a ruby and vanadium can produce the green in an emerald, depending on the crystal structure and bonding characteristics. Buyers must be aware that Alexandrite can now be grown in a lab, the first ones once sold as "Morning Glory" (now discontinued). A fair amount of color change was obtained in corundum ("An extremely hard mineral, aluminum oxide, Al2O3, sometimes containing iron, magnesia, or silica, that occurs in gem varieties such as ruby and sapphire and in a common black, brown, or blue form used chiefly in abrasives.") These lab created stones are attrative and show a fair amount of color change, but the chrysoberyl form is the only authentic Lab Grown Alexandrite and is clearly more beautiful and desireable. Be careful when buying this stone as there are unscupulous dealers that may try to pass off the cheaper, inferior corundum simulation.

The most rare gemstone in the world is not Alexandrite, but another stone called Painite. There are only a handful of examples in the entire world, and almost all are located in museums, I would think it has to be that, but I could be wrong "_

no...moon rocks are a million times more expensive and if they bring back some samples from mars they will be even more than that