Pistol Packing

Pistol Packing (or Missing Laser Pistol) is an unmarked quest in Fallout: New Vegas.

Detailed walkthrough
Knight Torres, the quartermaster for the Brotherhood of Steel in the Hidden Valley bunker, will mention that she is missing one laser pistol from her inventory, which you can volunteer to help find. After speaking to her, head next door to the firing range and speak to the paladin sitting at the desk there. (If the paladin range master isn't at the firing range desk, try going down to the deck below and stepping into the large bedroom where he should be sleeping and speak to him.) Mention the pistol, and the paladin will mention that Initiate Stanton was the last one to check it out, but signed it back in. It is necessary to do this before talking to Stanton, or else he will claim that he doesn't know anything about it.

Initiate Stanton
Stanton can be found wandering around the first floor of the bunker or at the classroom during day time. At night, Stanton will be inside the initiate barracks, which is opposite of the long, oval-shaped hallway from the firing range. When you speak to him, mention the pistol he checked out. He will admit about how he and Watkins went out to the Scorpion Gulch for a "training exercise." Once he and Watkins realized the scorpions were more than they could handle, they ran away and he dropped the pistol in the confusion. If you mention the pistol being checked back in, he tells you that he falsified the records. From here, you can volunteer to retrieve the pistol.

Scorpion Gulch
Scorpion Gulch is just southeast through a broken fencing line from the bunker. After going through the gulch, the missing laser pistol will be on top of a rock, in the middle of the lowest part of the gulch. The gulch will usually have various scorpions roaming around the area.

Conclusion
Once you obtain the pistol, return to Torres. She will have repaired a broken tri-beam laser rifle, and will give it to you for free. You will also receive positive reputation among the Brotherhood of Steel.

Bugs

 * At the end of the missing laser quest, the tri-beam laser rifle received as a reward will be bugged. Do not place it in the same inventory with another tri-beam laser rifle, as it will be replaced by the one received from Torres.
 * The "dead" wastelander could potentially be alive and fight the scorpions that occupy the gulch with an invisible varmint rifle. He will still drop the normal loot upon death.
 * A corpse may not actually be present to mark the rock: if not, it's the large one at the bottom of the "bowl".
 * After speaking with Quartermaster Knight Torres to begin the quest, if you ask Initiate Stanton where the laser pistol is before speaking with the paladin at the firing range desk, Stanton denies any knowledge of the pistol, and the paladin at the firing range desk can't be found to correct the quest. Entirely exiting the bunker to the outside and re-entering may correct the missing quartermaster.
 * Possible solution: Talk to Initiate Stanton and go through all the dialogue options, then make your way to the shooting range. Talk to Knight Torres, if the dialogue does not show up to turn in the missing laser pistol. Save your game, then try talking to her again.