We present a novel medical imaging modality based on optical coherence tomography (OCT) that enables in vivo 3D tomography at acquisition rates up to 1 MHz. Line field parallel swept source interferometric imaging (LPSI) combines line-field swept source OCT with modulation of the interferometric signal in spatial direction for full range imaging. This method enables high speed imaging with cost-effective and commercially available technology. We explain the realization of the LPSI setup, acquisition, and postprocessing and finally demonstrate 3D in vivo imaging of human nail fold. To the best of our knowledge, sensitivity and depth penetration are competitive with respective point scanning OCT methods at a comparable wavelength. Measured maximum sensitivity is 98.5 dB for 100 kHz and 90 dB for 1 MHz. Together with the significantly relaxed technological requirements regarding detection and swept source technology, LPSI might be a promising concept for future diagnostic OCT imaging.