Chain rooms are rooms in the Thirteen Towers where a chain is rooted. By destroying the base of the chain in the chain room, you will destroy that chain. Thus, every chain room in a Tower must be visited before you can access the Master's chamber. The chain can be destroyed with any of your weapons. It will usually take three hits.
A chain room is locked by a orange mechanism. To unlock the door, you must grapple the center of it with the Oraclos Chain and pull. As you pull, you will see a notch/indicator thing that shows you how close you are to unlocking the door. This indicator must be moved from pointing to the top to the left. However, if you let go before it is done, it will start to move back up. This makes it a good idea to kill any enemies in the immediate area first.
Chain rooms can be found by following a chain either from the Master's door or from wherever you see a chain in the Tower. The chain will lead through a hole above the door, which makes it easy to see if you've destryed the chain or not. Even after unlocking the door, it is possible to get distracted with enemies and forget to destroy the chain.