A high-resolution x-ray spectrometer was coupled with an ultrafast x-ray streak camera to produce time-resolved line shape spectra measured from hot, solid-density plasmas. A Bragg crystal was placed near laser-produced plasma to maximize throughput; alignment tolerances were established by ray tracing. The streak camera produced single-shot, time-resolved spectra, heavily sloped due to photon time-of-flight differences, with sufficient reproducibility to accumulate photon statistics. The images are time-calibrated by the slope of streaked spectra and dewarped to generate spectra emitted at different times defined at the source. The streaked spectra demonstrate the evolution of spectral shoulders and other features on ps timescales, showing the feasibility of plasma parameter measurements on the rapid timescales necessary to study high-energy-density plasmas.