The performance of today’s in-memory indexes is bottlenecked by the memory latency/bandwidth wall. Processing-in-memory (PIM) is an emerging approach that potentially mitigates this bottleneck, by enabling low-latency memory access whose aggregate memory bandwidth scales with the number of PIM nodes. There is an inherent tension, however, between minimizing inter-node communication and achieving load balance in PIM systems, in the presence of workload skew. This paper presents PIM-tree, an ordered index for PIM systems that achieves both low communication and high load balance, regardless of the degree of skew in data and queries. Our skew-resistant index is based on a novel division of labor between the host CPU and PIM nodes, which leverages the strengths of each. We introduce push-pull search, which dynamically decides whether to push queries to a PIM-tree node or pull the node’s keys back to the CPU based on workload skew. Combined with other PIM-friendly optimizations (shadow subtrees and chunked skip lists), our PIM-tree provides high-throughput, (guaranteed) low communication, and (guaranteed) high load balance, for batches of point queries, updates, and range scans. We implement PIM-tree, in addition to prior proposed PIM indexes, on the latest PIM system from UPMEM, with 32 CPU cores and 2048 PIM nodes. On workloads with 500 million keys and batches of 1 million queries, the throughput using PIM-trees is up to 69.7X and 59.1x higher than the two best prior PIM-based methods. As far as we know these are the first implementations of an ordered index on a real PIM system.