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Volatiles from the solar nebula are known to be present in Earth's deep mantle. The core also may contain solar nebula‐derived volatiles, but in unknown amounts. Here we use calculations of volatile ingassing and degassing to estimate the abundance of primordial³He now in the core and track the rate of³He exchange between the core and mantle through Earth history. We apply an ingassing model that includes a silicate magma ocean and an iron‐rich proto‐core coupled to a nebular atmosphere of solar composition to calculate the amounts of³He acquired by the mantle and core during accretion and core formation. Using experimentally determined partitioning between core‐forming metals and silicate magma, we find that dissolution from the nebular atmosphere deposits one or more petagrams of³He into the proto‐core. Following accretion,³He exchange depends on the convective history of the coupled core‐mantle system. We combine determinations of the present‐day surface³He flux with estimates of the present‐day mantle³He abundance, mantle and core heat fluxes, and our ingassed³He abundances in a convective degassing model. According to this model, the mantle³He abundance is evolving toward a statistical steady state, in which surface losses are compensated by enrichments from the core.