Theory predicts that, with an ultrashort and extremely bright coherent X-ray pulse, a single diffraction pattern may be recorded from a large macromolecule, a virus or a cell before the sample explodes and turns into a plasma. Here we report the first experimental demonstration of this principle using the FLASH soft-X-ray free-electron laser. An intense 25 fs, 4×10¹³ W cm⁻² pulse, containing 10¹² photons at 32 nm wavelength, produced a coherent diffraction pattern from a nanostructured non-periodic object, before destroying it at 60,000 K. A novel X-ray camera assured single-photon detection sensitivity by filtering out parasitic scattering and plasma radiation. The reconstructed image, obtained directly from the coherent pattern by phase retrieval through oversampling shows no measurable damage, and is reconstructed at the diffraction-limited resolution. A three-dimensional data set may be assembled from such images when copies of a reproducible sample are exposed to the beam one by one.