Core-periphery structure is an important network feature where the network is broken into two components: a densely connected core and a loosely connected periphery. In this work, we propose a divide-and-conquer algorithm to identify the core-periphery structure in large networks. By finding this structure on much smaller sub-samples of the network and then combining the results across sub-samples, this method yields fast and accurate core-periphery labels. Additionally, the method provides a measure of the statistical significance of the structure. We apply our approach to synthetic data to find the algorithm's detection limit and on a real-world network with more than 35,000 nodes.