Systems performing large data-parallel computations, including online analytical processing (OLAP) systems like Druid and search engines like Elasticsearch, are increasingly being used for business-critical real-time applications where providing low query latency is paramount. In this paper, we investigate an underexplored factor in the performance of data-parallel queries: their parallelism. We find that to minimize the tail latency of data-parallel queries, it is critical to place data such that the data items accessed by each individual query are spread across as many machines as possible so that each query can leverage the computational resources of as many machines as possible. To optimize parallelism and minimize tail latency in real systems, we develop a novel parallelism-optimizing data placement algorithm that defines a linearly-computable measure of query parallelism, uses it to frame data placement as an optimization problem, and leverages a new optimization problem partitioning technique to scale to large cluster sizes. We apply this algorithm to popular systems such as Solr and MongoDB and show that it reduces p99 latency by 7-64% on data-parallel workloads.