RFID (Radio-Frequency IDentification) is a key emerging technology for supply-chain monitoring and detection of counterfeit and grey-market goods. The most prevalent RFID tags are, however, simply \"Wireless barcodes,\" themselves vulnerable to cloning and counterfeiting. While continuous monitoring can, in principle, detect cloning attacks, real-world supply chains often contain significant blind zones where tag readings are unavailable, allowing attackers to inject counterfeit goods with cloned tags into supply chains undetectably. This paper introduces tailing, a novel approach, both simple and practical, for detecting cloned RFID tags in supply chains. With tailing, RFID readers write random values to tags as they pass through a supply chain, creating in each tag a tail composed of random values.