We have demonstrated single-shot continuously time-resolved MeV ultrafast electron diffraction using a static single crystal gold sample. An MeV high density electron pulse was used to probe the sample and then streaked by an rf deflecting cavity. The single-shot, high quality, streaked diffraction pattern allowed structural information within several picoseconds to be continuously temporally resolved with an approximately 200 fs resolution. The temporal resolution can be straightforwardly improved to 100 fs by increasing the streaking strength. We foresee that this system would become a powerful tool for ultrafast structural dynamics studies.