We present Atacama Large Millimeter–Submillimeter Array (ALMA) observations of CK Vulpeculae which is identified with ‘Nova Vulpeculae 1670’. They trace obscuring dust in the inner regions of the associated nebulosity. The dust forms two cocoons, each extending ~5 arcsec north and south of the presumed location of the central star. Brighter emission is in a more compact east–west structure (2 arcsec × 1 arcsec) where the cocoons intersect. We detect line emission in NH2CHO, CN, four organic molecules, and C17O. CN lines trace bubbles within the dusty cocoons; CH3OH a north–south S-shaped jet; and other molecules a central cloud with a structure aligned with the innermost dust structure. The major axis of the overall dust and gas bubble structure has a projected inclination of ~24° with respect to a 71 arcsec extended ‘hourglass’ nebulosity, previously seen in H a. Three cocoon limbs align with dark lanes in the inner regions of the same H a images. The central 2 arcsec × 1 arcsec dust is resolved into a structure consistent with a warped dusty disc. The velocity structure of the jets indicates an origin at the centre of this disc and precession with an unknown period. Deceleration regions at both the northern and southern tips of the jets are roughly coincident with additional diffuse dust emission over regions approximately 2 arcsec across. These structures are consistent with a bipolar outflow expanding into surrounding high-density material. We suggest that a white dwarf and brown dwarf merged between 1670 and 1672, with the observed structures and extraordinary isotopic abundances generated as a result.