The ability to image cell chemistry at the nanoscale is key for understanding cell biology, but many optical microscopies are restricted by the ~250nm diffraction limit. Electron microscopy and super-resolution fluorescence techniques beat this limit, but rely on staining and specialised labelling to generate image contrast. It is challenging, therefore, to obtain information about the functional chemistry of intracellular components. Here we demonstrate a technique for intracellular label-free chemical mapping with nanoscale (~30nm) resolution. We use a probe-based optical microscope illuminated with a mid-infrared laser whose wavelengths excite vibrational modes of functional groups occurring within biological molecules. As a demonstration, we chemically map intracellular structures in human multiple myeloma cells and compare the morphologies with electron micrographs of the same cell line. We also demonstrate quantitative and label-free mapping at multiple wavelengths chosen to target the chemical signatures of macromolecules, including proteins and nucleic acids, in a way that can be used to identify biochemical markers in the study of disease and pharmacology.