This exact thing happened to me on a trip last year in the north woods of Wisconsin. A guy was out chopping wood and his dog started to chase me. It was a German Shepherd and it was obvious right away that I couldn't outrun the dog (an uneasy feeling to say the least).
My only choice was to do what Flightgear said and to stop and stand still as the dog approached. He ran past me then stood and barked at me from 10 feet away. This went on for 30 seconds until the owner showed up.
I run outdoors at home and on trips every chance I get and this is the only run in I've ever had. Could have been much worse and it keeps me more aware to this day!
Boat