Hat of the People
It can be found in a room in an average locked floor safe on the second floor of the abandoned apartments (green door, to the left if you are facing Haven) under a table in a floor safe with average lock in the Uptown portion of the Pitt.
This item is present within Fallout 3's files before the add-on's release. However, it is cut content and, without The Pitt add-on, is only obtainable with console commands. If the item is obtained within The Pitt and the add-on is then uninstalled, the hat will remain in the player character's inventory.
The same apartment containing the safe with the hat also has several Chinese assault rifles and a small stockpile of ammunition & Pre-War money. This may indicate that the people living in this apartment were Chinese infiltrators.
ps3 pc While wearing the Hat of the People, the Pip-Boy lists its effect as "combat jumpsuit Small guns +5". [verified]