The Galileo probe showed that Jupiter's atmosphere is severely depleted in neon compared to protosolar values. We show via ab initio simulations of the partitioning of neon between hydrogen-helium phases that the observed depletion can be explained by the sequestration of neon into helium-rich droplets within the postulated hydrogen-helium immiscibility layer of the planets interior. We also demonstrate that this mechanism will not affect argon explaining the observed lack of depletion of this gas. This provides strong indirect evidence for hydrogen-helium immiscibility in Jupiter.