The first successful operation of a neutron interferometer with a separate beam-recombining crystal is reported. This result was achieved at the neutron interferometry setup S18 at the ILL in Grenoble by a collaboration between TU Wien, ILL, Grenoble, and INRIM, Torino. While previous interferometers have been machined out of a single-crystal block, in this work two crystals were successfully aligned on nanoradian and picometre scales, as required to obtain neutron interference. As a decisive proof-of-principle demonstration, this opens the door to a new generation of neutron interferometers and exciting applications.