Intermediation chains represent a common pattern of trade in over-the-counter markets. We study a classic problem impeding trade in these markets: an agent uses his market power to inefficiently screen a privately informed counterparty. We show that, generically, if efficient trade is implementable via any incentive-compatible mechanism, it is also implementable via a trading network that takes the form of a sufficiently long intermediation chain. We characterize information sets of intermediaries that ensure this striking result. Sparse trading networks featuring long intermediation chains might thus constitute an efficient market response to frictions, in which case no regulatory action is warranted.