So according to this wikihow page, Chaining is encountering the same Pokémon repeatedly to better your chances of finding a shiny version. You have to KO the non-shinies until you find what your looking for.There are also a few other things of note, like distance of the next chain and ways the chain might be broken. But this speaks of chaining in fields of tall grass with the use of repel and the PokéRadar.
But in Eterna Forest, there's the old chateu, inside aside from the Rotom which you only encounter in the TV in one of the rooms, you get only Gastlys
So unless i'm mistaken about the basic concept of Chaining, it should be rather easy getting a shiny gastly there – not needing repel or the PokéRadar. So can I chain for a shiny gastly in the Old Chateu?
Edit: Apparently you can find Hauntar and even Gengar, but they are very rare and only appear in certain rooms with certain conditions.
Best Answer
Chaining requires the PokéRadar. Just encountering the same Pokémon multiple times in a row will not increase the chances of finding a shiny Pokémon.