TripleRush is a parallel in-memory triple store designed to address the need for efficient graph stores that answer queries over large-scale graph data fast. To that end it leverages a novel, graph-based architecture. Specifically, TripleRush is built on our parallel and distributed graph processing framework Signal/Collect. The index structure is represented as a graph where each index vertex corresponds to a triple pattern. Partially matched copies of a query are routed in parallel along different paths of this index structure. We show experimentally that TripleRush takes less than a third of the time to answer queries compared to the fastest of three state-of-the-art triple stores, when measuring time as the geometric mean of all queries for two benchmarks. On individual queries, TripleRush is up to three orders of magnitude faster than other triple stores.