You acquire this quest by speaking to G'axir the Seer in the Blade and Stars tavern in Baldur's Gate. After providing some foreshadowing of your heritage and terrible fate he tells you that he wants you to bring him a Sphene Gem and suggests getting one from the Greater Basilisk in Baldur's Gate. There are many Sphene Gems in the game but, while any of them will do, taking the one from the Basilisk is convenient. This Basilisk is also the target of the Basilisk on the Loose quest. It is located in the northern warehouse in Baldur's Gate Docks.
Killing the Basilisk Edit
To kill the Basilisk you can use Potion of Mirrored Eyes, Protection from Petrification spell, or items that provide a bonus to save vs petrification rolls, like Adoy's Belt, Claw of Kazgaroth or protection Ring/Cloak. It may be best to put put protective spells and items on one Fighter who will face the Basilisk in close combat and have other party members attack with ranged weapons to minimize the risk of petrification. Once it is dead you can loot the Sphene Gem from its body.