Supply chain traceability refers to product tracking from the source to customers, demanding transparency, authenticity, and high efficiency. In recent years, blockchain has been widely adopted in supply chain traceability to provide transparency and authenticity, while the efficiency issue is understudied. In practice, as the numerous product records accumulate, the time- and storage- efficiencies will decrease remarkably. To the best of our knowledge, this paper is the first work studying the efficiency issue in blockchain-based supply chain traceability. Compared to the traditional method, which searches the records stored in a single chunk sequentially, we replicate the records in multiple chunks and employ parallel search to boost the time efficiency. However, allocating the record searching primitives to the chunks with maximized parallelization ratio is challenging. To this end, we model the records and chunks as a bipartite graph and solve the allocation problem using a maximum matching algorithm. The experimental results indicate that the time overhead can be reduced by up to 85.1% with affordable storage overhead.