Solve Phil's Canine Conundrum

Go to the Casino area of Junktown. To the right of the entrance to the area there are a pair of people trying unsuccessfully to enter their house. The reason: a dog.

Simply wear a Leather Jacket (which will remind it of it's former master) or give the pooch some Iguana-on-a-stick to solve the quest and let the couple enter their house unmolested. There is a 100 experience reward for doing this, as well as the couple's thanks and a pet dog named Dogmeat that will follow you everywhere and has lots of nifty bite attacks in combat.

Reward
100 XP and Dogmeat!

Behind the scenes
The whole ordeal with the dog is a reference to Mad Max and A Boy and His Dog. The name Dogmeat is used for the boy's dog, while the leather jacket-wearing fool is a nod to Mel Gibson's role as Max Rockatansky.