I believe the prize goes to Chain Fishing. You stand in the same spot, and have a Pokemon with Suction Cups or Sticky Hold lead your party. You then cast your line, any Rod, over and over and over again. As long as you don't move, and always reel in a Pokemon, your Shiny chance will increase each cast. When you do find your Shiny, it resets (whether you catch it, run from it, defeat it, or, obviously, it defeats you). I think the average is somewhere around 40 casts to a Shiny? I haven't done it myself.
The Sticky Hold/Suction Cups part is important to guarantee a Pokemon will bite on every cast.