Alternatively, it is given to you by Motor-Runner if you decide to tell Hsu that Motor-Runner is "dead."
You can also pickpocket it. First reverse pickpocket a headgear with 3 or higher DT, and go to another zone and wait for 3 days. Then return to pickpocket it. Hsu will accept it like you have arrangement with Motor-Runner. You can use it when you can't speak with him and want to keep him alive and still complete the mission.
Notes
You must give it to Colonel Hsu to end the associated mission, you earn NCR fame and caps but lose the helmet unless it bugs. Freeing the ranger Bryce Anders and speaking to Hsu is enough to go from "liked" status with the NCR to "idolized" (regardless of dialogue choice), so turning over the helmet is entirely optional due to numerous other ways to raise reputation.
While wearing Motor-Runner's Helmet, non-player characters will occasionally comment on the fact that Motor-Runner is dead as you walk past.
Due to its quest item status, it can't be tossed even when broken. Without the aid of console commands this item can remain indefinitely in the Courier's inventory.
Bugs
Xbox 360 Sometimes the helmet will give a +2 Perception and a +10 Melee weapons bonus. [verified]
PC Motor-Runner's Helmet will sometimes remain in the Courier's inventory even after the associated quest is completed. It is a quest item: it cannot be dropped, placed into a container or given to a companion. Simple console commands can remove this item from the Courier's inventory. [verified]
Xbox 360 Killing Motor-Runner without having been assigned to do so will cause you to fail a quest. HOWEVER, you can still give the helmet to Hsu for the quest XP (the helmet won't be removed from your inventory though the option appears to exist to drop it. Clicking the "Drop" button will not drop the helmet, and you will simply get the Quest Item error message). [verified]
Xbox 360 Sometimes, in the add-on Dead Money, when this helmet is in your inventory, the game will crash when you find the 'source' of the signal, and the 'trap' is sprung. [verified]
Sometimes the helmet will give a +2 Perception and a +10 Melee weapons bonus. [verified]
