The source of and timing of delivery of the volatile elements to Earth is a question that is fundamental to understanding how our planet evolved. Here, we show that primitive meteorites have resolved mass-independent Zn isotope anomalies from the terrestrial reservoir. Carbonaceous chondrites (CC), likely originating from the outer Solar System are distinct from non-CC, and Earth is intermediate between these two components. Modelling based on these data indicates that around 30% of Earth's budget of Zn and other moderately volatile material derives from the participation of 6% of CC-like materials during Earth's accretion, with the remaining coming from NC meteorites. This implies that, despite the relatively minor mass of Earth thought to derive from CC-like material, the CC component of Earth was relatively and significantly volatile-enriched; this is in line with the observation that the terrestrial elemental abundance pattern of moderately volatile elements could be explained by a carbonaceous source, and with the carbonaceous chondrite-like isotopic budget of more volatile-rich material accreted later in Earth's accretion history (e.g. Hg, Se, N, noble gases).