YouTuber ToyDualer has posted a video explaining how chain fishing works, and how it increases the rate of shiny Pokemon appearances significantly in Omega Ruby and Alpha Sapphire.
Normally, trainers have only a 1-in-4096 chance to encounter a shiny Pokemon, but chain fishing drastically increases the rate at which these creatures appear.
Chain fishing is basically just standing in the same spot and fishing there over and over again until a shiny Pokemon appears. For this to work, you'll need a Pokemon with either the sticky hold or suction cups ability, both of which increase the liklihood that you'll find a wild Pokemon when you fish.
You can find a gulpin on Route 110 with the sticky hold ability or head to the Battle Resort and use a super rod to find a high level remoraid with the hustle ability. When your remoraid evolves into octillery, it will gain the suction cups ability. Place your Pokemon with the suction cups or sticky hold ability at the front of your party when you go to chain fish, as the effects will not work if they're not.
It won't matter if your Pokemon faints, as long as its at the front of your party its ability will work. With the right Pokemon at the front of your team and an Old, Good, or Super rod, head to some water and start fishing. So long as you don't move around or reload the game, you'll find a shiny Pokemon sooner or later.
You can fight or run from the battles you encounter but catching a Pokemon will break the chain. On average, it will take about 20 minutes to find a shiny Pokemon using this method.
The chain fishing video is below.