This paper studies the strategy of adopting blockchain technology (BT) in two supply chains, each consisting of one manufacturer and one retailer. We find that the adoption of BT in supply chains is related to consumers' traceability awareness and the blockchain-based traceability cost-sharing between the manufacturer and retailer. Specifically, when both consumers' traceability awareness and the proportion of the blockchain-based traceability cost borne by each retailer are low or moderate, the equilibrium strategy could be that one or both supply chains adopt BT. Moreover, when one supply chain adopts BT, the other may be a free rider. When both supply chains adopt BT, one supply chain can gain a competitive advantage when its retailer shares more of the blockchain-based traceability cost than the rival. Counterintuitively, when traceability awareness is high, neither of the two supply chains should adopt BT.