George Stigler coined the name “the Coase theorem” to refer to the idea proposed by Ronald Coase in “The Problem of Social Cost” (Coase in Journal of Law and Economics 3:1–44, 1960) of a negotiated solution to externalities. But the name contained two errors: it was not a theorem, and it was not Coase’s message, which insisted rather on the role of transaction costs. In microeconomics, the unidentified object named “the Coase theorem”, however, became central. Stigler, initially unconvinced by Coase’s criticism of the Pigovian analysis of externalities (Coase in Journal of Law and Economics 2:1–40, 1959), was converted in one night according to his 1988 autobiography. He stated the “Coase theorem” in the third edition of his Theory of Price, but made it rest only on examples. This chapter examines the meaning of his “Coase theorem”, both from an analytical perspective and as regards its theoretical implications.