Identification of chemical compounds by vibrational spectroscopy at infrared wavelengths requires macroscopic samples: the spatial resolution is diffraction-limited to a scale of about half the wavelength, or about five micrometres, The scanning near-field optical microscope(1,2), however, can reveal sub-wavelength detail because it uses near-field probing rather than beam focusing. Here we demonstrate the use of the aperture-less approach to scanning near-field optical microscopy(3-6) to obtain contrast in vibrational absorption on a scale of about 100 nanometres, about one-hundredth of a wavelength. We record infrared scattering from the tip of an atomic force microscope scanned over a composite polymer film. At the boundary between different polymers we observe contrast changes owing to changes in vibrational absorption. The contrast is strongly enhanced in the near field of the probe tip, which we interpret as evidence of surface-enhanced infrared absorption(7). When extended to multi-wavelength operation, this approach should enable imaging of chemical composition at nanometre resolution.