Software-Defined Internet Exchange Points (SDXes) promise to significantly increase the flexibility and function of interdomain traffic delivery on the Internet. Unfortunately, current SDX designs cannot yet achieve the scale required for large Internet exchange points (IXPs), which can host hundreds of participants exchanging traffic for hundreds of thousands of prefixes. Existing platforms are indeed too slow and inefficient to operate at this scale, typically requiring minutes to compile policies and millions of forwarding rules in the data plane. We motivate, design, and implement iSDX, the first SDX architecture that can operate at the scale of the largest IXPs. We show that iSDX reduces both policy compilation time and forwarding table size by two orders of magnitude compared to current state-of-the-art SDX controllers. Our evaluation against a trace from one of the largest IXPs in the world found that iSDX can compile a realistic set of policies for 500 IXP participants in less than three seconds. Our public release of iSDX, complete with tutorials and documentation, is already spurring early adoption in operational networks.