We demonstrate Fourier transform infrared nanospectroscopy (nano-FTIR) based on a scattering-type scanning near-field optical microscope (s-SNOM) equipped with a coherent-continuum infrared light source. We show that the method can straightforwardly determine the infrared absorption spectrum of organic samples with a spatial resolution of 20 nm, corresponding to a probed volume as small as 10 zeptoliter (10(-20) L). Corroborated by theory, the nano-FTIR absorption spectra correlate well with conventional FTIR absorption spectra, as experimentally demonstrated with poly(methyl methacrylate) (PMMA) samples. Nano-FTIR can thus make use of standard infrared databases of molecular vibrations to identify organic materials in ultrasmall quantities and at ultrahigh spatial resolution. As an application example we demonstrate the identification of a nanoscale PDMS contamination on a PMMA sample.