In three recent ICSID cases, claimants have sought to rely on customary international law as a separate head of claim to claims of breach of obligations arising under either an investment treaty or an investment contract. This article examines the extent to which claims under customary international law might fall within the scope of jurisdiction of an ICSID tribunal, by reference to the decided cases. It suggests that the starting point of the analysis must be the scope of consent given in the arbitration clause. In a claim brought pursuant to a contract, it might also be relevant to consider the applicable law of the contract, since that law might incorporate customary international law. While this analysis (and the decided cases) suggest that self-standing claims based on custom in ICSID arbitration are not beyond the realm of possibility, the author suggests that there are likely to be challenges for investors in relying on customary international law as a basis of a claim. Where consent to arbitration is found in an investment treaty, it might be argued that the treaty standard is lex specialis and, in any event, might not differ in any material way from the customary standard. Where consent to arbitration is found in an investment contract with an applicable law that incorporates customary law, there may be questions as to whether an investor is entitled to directly invoke custom. These questions are likely to be explored in future cases, and their answers are likely to depend on the particular circumstances in which they arise.