Heart of the Outsider are very rare stones used to upgrade the weapon Chaos Blade into Stranger. In-game, it can only be found twice per playthrough (although it is not confirmed if you can find them anywhere else). It is found in the treasure chest behind Dagran when the player first starts the game, and the second one during the Epilogue in Chapter 43. The chest is in the same room where the Statue of the Reptid Queen resides, and is at the leftmost part of that room. You have to use the Horace's Ring on the wall to reveal a hidden alcove where the chest is.
There is also a chance of winning a Heart of the Outsider in the Deathmatch Multiplayer.