For many Internet services, reducing latency improves the user experience and increases revenue for the service provider. While in principle latencies could nearly match the speed of light, we find that infrastructural inefficiencies and protocol overheads cause today's Internet to be much slower than this bound: typically by more than one, and often, by more than two orders of magnitude. Bridging this large gap would not only add value to today's Internet applications, but could also open the door to exciting new applications. Thus, we propose a grand challenge for the networking research community: a speed-of-light Internet. To inform this research agenda, we investigate the causes of latency inflation in the Internet across the network stack. We also discuss a few broad avenues for latency improvement.