There exists a conspicuous gap of knowledge about the organization of life at mesoscopic levels. Ultra-fast coherent diffractive imaging with X-ray free-electron lasers can probe structures at the relevant length scales and may reach sub-nanometer resolution on micron-sized living cells. Here we show that we can introduce a beam of aerosolised cyanobacteria into the focus of the Linac Coherent Light Source and record diffraction patterns from individual living cells at very low noise levels and at high hit ratios. We obtain two-dimensional projection images directly from the diffraction patterns, and present the results as synthetic X-ray Nomarski images calculated from the complex-valued reconstructions. We further demonstrate that it is possible to record diffraction data to nanometer resolution on live cells with X-ray lasers. Extension to sub-nanometer resolution is within reach, although improvements in pulse parameters and X-ray area detectors will be necessary to unlock this potential.