The Gibbering Gemstone is an item from Diablo 3, similar to the Black Mushroom, used to craft the Staff of Herding (the item you'll need if you want to enter the Pony Level). Many Diablo 3 players ask themselves where to find the Gibbering Gemstone or how to find it. In order to find the gemstone you'll need to go to Act 3, in the area called Fields of Slaughter. There is a rare dungeon called Caverns of Frost can be generated (if you are lucky). Be advised that there is another rare dungeon, Icefall Caves, similar in appearance with the Caverns of Frost. Do NOT enter that dungeon to get the Gibbering Gemstone, because you won't find it there.
So, once you found the Caverns of Frost dungeon, look for a unique boss named Chiltara, that can be found in the Caverns of Frost level 2 (but he can spawn in level one also I believe). The boss is a random one, so in some cases you can clear the whole dungeon without finding him and you'll need to the whole thing all over again. I was very lucky when I found the Gibbering Gemstone, it just dropped during my first Diablo 3 run. A friend of mine farmed for it for hours, so it's just a matter of luck, like the most of item hunting process in Diablo 3 is.