Using the Eris zoom-in cosmological simulation of assembly of a Milky Way analog , we study the chemical enrichment of stars due to accretion of metal-enriched gas from the interstellar medium during the Galaxy ’ s development . We consider metal-poor and old stars in the Galactic halo and bulge through the use of stellar orbits , gas density and metallicity distributions in Eris . Assuming spherically symmetric Bondi-Hoyle accretion , we find that halo and bulge stars accrete metals at the rate of about 10 ^ { -24 } M _ { \odot } yr ^ { -1 } and 10 ^ { -22 } M _ { \odot } yr ^ { -1 } , respectively , at redshifts z \lesssim 3 , but this accretion rate increases roughly a hundred-fold to about 10 ^ { -20 } M _ { \odot } yr ^ { -1 } at higher redshifts due to increased gas density . Bulge and halo stars accrete similar amounts of metals at high redshifts when kinematically distinct bulge and halo have not yet developed , and both sets of stars encounter a similar metal distribution in the ISM . Accretion alone can enrich main-sequence stars up to [ \mathrm { Fe } / \mathrm { H } ] \sim - 2 in extreme cases , with the median enrichment level due to accretion of about [ \mathrm { Fe } / \mathrm { H } ] \sim - 6 to -5 . Because accretion mostly takes place at high redshifts , it is \alpha -enriched to [ \alpha / \mathrm { Fe } ] \sim 0.5 . We find that accretive metal enrichment is sufficient to affect the predicted metallicity distribution function of halo stars at [ \mathrm { Fe } / \mathrm { H } ] < -5 . This can hinder attempts to infer natal chemical environment of metal-poor stars from their observed enrichment . Peculiar enrichment patterns such as those predicted to arise from pair-instability supernovae could help in disentangling the natal and accreted metal content of stars .