The Talking Head is a Fallout 2 special encounter. You can "meet" him randomly in the Wastelands. He is actually a talking version of the big stone head of the Vault Dweller in the Arroyo village center. If you talk to him and tell him you are the Chosen One, he disagrees and begins an argument back and forth that lasts for 12 hours. He will then concede that you have proven yourself to be the Chosen One and give you a monument chunk as a reward.
If you happen to be a kleptomaniac, and steal from the big stone head, you'll find 3 or so more monument chunks as an award. However, if you have Steal less than 95%, you won't get very far away with it, as the Vault Dweller's head dishes out a world of hurt, dealing about 14,000 points of damage, and melting you.