The links in a toilet chain will constantly twist and become tangled up because the chain is too long. You can repair it by either adjusting the chain or the trip lever. Left alone, the twisted chain will interfere with how the flapper seats, and could potentially lead to an increase in your water bill by wasting tank water.
Causes
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The flushing components inside the toilet are situated so that the chain should be a certain length. When the chain is too long, the extra length causes it to twist, catch itself or even get stuck underneath the flapper before the flapper seats after the toilet flushes. The same thing will happen, whether you have a plastic or metal chain. Even though it may not occur with every single flush, as long as the chain is too long, the problem will persist.
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Symptom
Your first clue that the chain has twisted is usually when you hear the tank constantly running after you flush the toilet. The twisted chain is preventing the flapper from seating, and allowing water to constantly escape from the tank, underneath the flapper. A common reaction is to shake the handle until the running stops. Shaking the handle will straighten the chain out, although it is just a temporary fix.
The Parts Involved
After you remove the lid and gaze into the tank, aside from the chain itself, the two other components that are involved are the flapper and the trip lever. The flapper is the rubber mechanism, usually red or black, that raises and lowers when the chain pulls on it. The other end of the chain is connected to the trip lever, which is the arm that connects to the handle.
Fixing the Problem
Adjust a chain that is too long, so that there is the least amount of slack between the trip lever and the flapper. Either remove the chain and cut off the extra links, or move the chain's connection with the trip lever down, further away from the flapper. The trip lever usually has a series of holes in it, so you may be able to hook the chain end into a different hole, if the chain itself is not overly long. Also, if the chain is not so long that it needs to be cut shorter, and the trip lever is bendable, you may be able to slightly bend the trip lever away from the flapper, and stretch the chain out.