Vibrational spectroscopy in the electron microscope would be transformative in the study of biological samples, provided that radiation damage could be prevented. However, electron beams typically create high-energy excitations that severely accelerate sample degradation. Here this major difficulty is overcome using an 'aloof' electron beam, positioned tens of nanometres away from the sample: high-energy excitations are suppressed, while vibrational modes of energies <1 eV can be 'safely' investigated. To demonstrate the potential of aloof spectroscopy, we record electron energy loss spectra from biogenic guanine crystals in their native state, resolving their characteristic C-H, N-H and C=O vibrational signatures with no observable radiation damage. The technique opens up the possibility of non-damaging compositional analyses of organic functional groups, including non-crystalline biological materials, at a spatial resolution of ∼10 nm, simultaneously combined with imaging in the electron microscope.