Giant radio pulses (GRPs) are sporadic bursts emitted by some pulsars, lasting a few microseconds. GRPs are hundreds to thousands of times brighter than regular pulses from these sources. The only GRP-associated emission outside radio wavelengths is from the Crab Pulsar, where optical emission is enhanced by a few percent during GRPs. We observed the Crab Pulsar simultaneously at X-ray and radio wavelengths, finding enhancement of the X-ray emission by $3.8pm0.7%$ (a 5.4$sigma$ detection) coinciding with GRPs. This implies that the total emitted energy from GRPs is tens to hundreds of times higher than previously known. We discuss the implications for the pulsar emission mechanism and extragalactic fast radio bursts.