We study r-process feasibility inside jets launched by a cold neutron star (NS) spiralling-in inside the core of a giant star, and find that such common envelope jets supernova events might be a significant source of heavy r-process elements in the early Universe. We run the stellar evolution code MESA to follow the evolution of low metalicity giant stars that swallow NSs during their late expansion phases and find that in some of the cases the NSs penetrate the core. The Bondi-Hoyle-Lyttleton (BHL) mass accretion rate onto a NS as it spirals-in inside the core is sufficiently high to obtain a neutron rich ejecta as required for the heavy r-process where the second and third r-process elements are synthesized. Due to the small radius of the NS the accretion is through an accretion disk and the outflow is in jets (or bipolar disk winds). The r-process nucleosynthesis takes place inside the jets. To account for the r-process abundances in the Galaxy we require that one in ten cases of a NS entering the envelope of a giant star ends as a CEJSN r-process event.