I have encountered 3 shinies and successfully caught 2 of them in 4th gen. None of them were through chaining.
The first one was in 2010 in HeartGold. It was a shiny Rattata in the Burned Tower. I thought it was cool how it was golden and it was in HeartGold. I named it "Goldie" I believe. Unfortunately I decided to evolve it into a Raticate without knowing what the shiny looks like and it looked lame imo. Just a slightly orangey-er shade of brown. I later traded it to Pearl, my favorite game.
The second was a pink Wooper in the Great Marsh in Pearl in 2011. It was incredibly risky to catch as you can imagine, but I caught it with 2 safari balls! This time I looked up what shiny Quagsire looked like and it is purple which is my favorite color, so I evolved it! I named it "Purpse".
The final 4th gen shiny I encountered was in 2012. I was starting to notice the lucky, coincidental pattern of encountering one shiny per year. I was fishing in Route 220 in Pearl trying to catch a Lanturn because I was trying to complete the Pokedex and I was too lazy to grind a Chinchou to evolve it. I knew Lanturn was rare, but it seemed to be taking a ridiculous amount of time to find one, I just kept hooking a ton of Chinchou. I joked that at that rate I was going to encounter a shiny Chinchou before I found a Lanturn. But then it happened! I quickly sent out my at-the-time level 50ish Weaville with False Swipe that I always have on my team now in case I run into a shiny. I used False Swipe, but unfortunately I didn't know that Chinchou could learn Take Down and it killed itself :( It turns out if it had been one level lower it wouldn't have even known Take Down.
Those are the only shinies I've encountered in gen 4 besides the Red Gyarados.