Carbon-enhanced metal-poor (CEMP) stars in the Galactic Halo display enrichments in heavy elements associated with either the s (slow) or the r (rapid) neutron-capture process (eg, barium and europium, respectively), and in some cases they display evidence of both. The abundance patterns of these CEMP-s/r stars, which show both Ba and Eu enrichment, are particularly puzzling, since the s and the r processes require neutron densities that are more than ten orders of magnitude apart and, hence, are thought to occur in very different stellar sites with very different physical conditions. We investigate whether the abundance patterns of CEMP-s/r stars can arise from the nucleosynthesis of the intermediate neutron-capture process (the i process), which is characterized by neutron densities between those of the s and the r processes. Using nuclear network calculations, we study neutron capture nucleosynthesis at different constant neutron densities n ranging from 10 7–10 15 cm− 3. With respect to the classical s process resulting from neutron densities on the lowest side of this range, neutron densities on the highest side result in abundance patterns, which show an increased production of heavy s-process and r-process elements, but similar abundances of the light s-process elements. Such high values of n may occur in the thermal pulses of asymptotic giant branch stars due to proton ingestion episodes. Comparison to the surface abundances of 20 CEMP-s/r stars shows that our modeled i-process abundances successfully reproduce observed abundance patterns, which could not be previously explained by s-process nucleosynthesis. Because the i-process models fit the abundances of CEMP-s/r stars so well, we propose that this class should be renamed as CEMP-i.