Modern, high-brightness electron beams such as those from plasma wakefield accelerators and free-electron laser linacs continue the drive to ever-shorter bunch durations. In low-charge operation (~20 pC), bunches shorter than 10 fs are reported at the Linac Coherent Light Source (LCLS). Though suffering from a loss of phase information, spectral diagnostics remain appealing as compact, low-cost bunch duration monitors suitable for deployment in beam dynamics studies and operations instrumentation. Progress in middle-infrared (MIR) imaging has led to the development of a single-shot, MIR prism spectrometer to characterize the corresponding LCLS coherent beam radiation power spectrum for few-femtosecond scale bunch length monitoring. In this Letter, we report on the spectrometer installation as well as the temporal reconstruction of 3 to 60 fs-long LCLS electron bunch profiles using single-shot coherent transition radiation spectra.