Evidence for the capture of nebular gases by planetary interiors would place important constraints on models of planet formation. These constraints include accretion timescales, thermal evolution, volatile compositions and planetary redox states(1-7). Retention of nebular gases by planetary interiors also constrains the dynamics of outgassing and volatile loss associated with the assembly and ensuing evolution of terrestrial planets. But evidence for such gases in Earth's interior remains controversial(8-14). The ratio of the two primordial neon isotopes, Ne-20/Ne-22, is significantly different for the three potential sources of Earth's volatiles: nebular gas(15), solar-wind-irradiated material(16) and CI chondrites(17). Therefore, the Ne-20/Ne-22 ratio is a powerful tool for assessing the source of volatiles in Earth's interior. Here we present neon isotope measurements from deep mantle plumes that reveal Ne-20/Ne-22 ratios of up to 13.03 +/- 0.04 (2 standard deviations). These ratios are demonstrably higher than those for solar-wind-irradiated material and CI chondrites, requiring the presence of nebular neon in the deep mantle. Furthermore, we determine a Ne-20/Ne-22 ratio for the primordial plume mantle of 13.23 +/- 0.22 (2 standard deviations), which is indistinguishable from the nebular ratio, providing robust evidence for a reservoir of nebular gas preserved in the deep mantle today. The acquisition of nebular gases requires planetary embryos to grow to sufficiently large mass before the dissipation of the protoplanetary disk. Our observations also indicate distinct Ne-20/Ne-22 ratios between deep mantle plumes and mid-ocean-ridge basalts, which is best explained by addition of a chondritic component to the shallower mantle during the main phase of Earth's accretion and by subsequent recycling of seawater-derived neon in plate tectonic processes.