In Chapter 5, when you reach the Merchant behind the Town Hall after rescuing Ashley from the church, there will be a request to take care of a “Savage Mutt”. The notice will tell you he can be found at the Village Chief’s Manor, but when you go there, he can’t be found. That’s because he’s moved on to the Village. Equip a flash grenade your strongest gun and go get him!
Initially, the dog will show up on the map at the Village Chief’s Manor.
However, once you go there, you’ll be able to hear it, but not find it. It has made its way back to the Village and you can find it there. Make sure everything is reloaded before you re-enter the Village and if you have a flash grenade on you, even better.