Obtain: Knight Torres in Hidden Valley.
Speak with Torres in the Brotherhood of Steel bunker and then offer your services to tell you about the missing laser gun (Image 1). Exit the store and go talk to the manager of the shooting gallery who is waiting just next door (Image 2). This will teach you that it was Apprentice Stanton who last used the missing gun. So go to the classrooms and question the young man to learn more (Image 3).
Stanton apparently lost the gun while fighting a horde of radscorpions, so exit the bunker and head southeast to Scorpion Gulch (Picture 4-5). There, eliminate the Scorpions then recover the laser gun on the central rock (Picture 6). You just have to bring it back to Torres to earn some reputation points.