A chain, when used in reference to the process of buying or selling a house, is a sequence of linked house purchases, each of which is dependent on the preceding and succeeding purchase.
Where no chain exists, it is called a chain-free property but only 10% of property transactions in the United Kingdom have no chain.
This situation is notorious for being liable to "break" if one of the transactions fails, for example due to financial difficulties, a change of heart, or the practice of gazumping or gazundering.
The failure of one member of the chain fouls the whole set of transactions.
Examples: A chain ends with a house being sold and not depending on existing owners buying a house to move into.