The red chain was a beta item, and it is not possible to get it in game. The item does exist, however, and you can obtain it through AR/pokesav (create a Pokemon holding it and use the GTS exploit.) There is no purpose for this item.
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What is a red chain?
Either cheat or "chain" 40 pokemon.
Of course
There are four shards in Pokemon Platinum- red, blue, green and yellow. They can all be found in the Underground.
you get it as a starter in diamond, pearl and platinum