Phonon polaritons in van der Waals materials can strongly enhance light-matter interactions at mid-infrared frequencies, owing to their extreme field confinement and long lifetimes(1-7). Phonon polaritons thus bear potential for vibrational strong coupling with molecules. Although the onset of vibrational strong coupling was observed spectroscopically with phonon-polariton nanoresonators(8), no experiments have resolved vibrational strong coupling in real space and with propagating modes. Here we demonstrate by nanoimaging that vibrational strong coupling can be achieved between propagating phonon polaritons in thin van der Waals crystals (hexagonal boron nitride) and molecular vibrations in adjacent thin molecular layers. We performed near-field polariton interferometry, showing that vibrational strong coupling leads to the formation of a propagating hybrid mode with a pronounced anti-crossing region in its dispersion, in which propagation with negative group velocity is found. Numerical calculations predict vibrational strong coupling for nanometre-thin molecular layers and phonon polaritons in few-layer van der Waals materials, which could make propagating phonon polaritons a promising platform for ultrasensitive on-chip spectroscopy and strong-coupling experiments. Real-space mid-infrared nanoimaging reveals vibrational strong coupling between molecules and propagating phonon polaritons in unstructured, thin hexagonal boron nitride layers, which could provide a platform for testing strong coupling and local control of chemical properties.