Radiation damage is considered to be the major problem that still prevents imaging an individual biological molecule for structural analysis. So far, all known mapping techniques using sufficient short wavelength radiation, be it x rays or high energy electrons, circumvent this problem by averaging over many molecules. Averaging, however, leaves conformational details uncovered. Even the anticipated use of ultrashort but extremely bright x-ray bursts of a free electron laser shall afford averaging over 106 molecules to arrive at atomic resolution. Here, we present direct experimental evidence for nondestructive imaging of individual DNA molecules. In fact, we show that DNA withstands coherent low energy electron radiation with deBroglie wavelength in the Ångstrom regime despite a vast dose of 108 electrons/nm2 accumulated over more than one hour.