Crystallization experiments on liquids with compositions similar to those of compact Type A, Type B1 and Type B2 refractory inclusions were conducted under controlled temperature and fO2 conditions. Application of the results to the compositions of coexisting Ti3+ -bearing fassaitic clinopyroxene + melilite pairs in natural inclusions shows that, if they crystallized at ~1509 K, they did so at log fO2 = −19.8 ± 0.9, only slightly below the equilibrium log fO2 of a partially condensed system of solar composition at the same temperature, −18.1−0.3+0.2, or IW-6.8. Fassaite is the only fO2 indicator that shows that anything in chondrites formed in a system that was close to solar in composition. Solar composition is so reducing that equilibrium calculations predict vanishingly small FeO/(FeO + MgO) ratios in the condensate until temperatures fall below 800 K, where significant oxidation of metallic iron and formation of fayalite in solid solution with previously condensed forsterite begin. The mechanism for the latter process is diffusion of Fe2+ through forsterite, but the diffusion rate is nearly zero at these temperatures. By comparison to what is achievable in a system of solar composition, the mean FeO/(FeO + MgO) ratio of the olivine in chondrules in unequilibrated ordinary chondrites (UOCs) is very high, ~0.15. Making such ratios in chondrule precursors by solar nebular processes requires sufficiently high fO2 for iron to become oxidized above temperatures where diffusion of Fe2+ becomes very slow. Two dynamic models for enrichment of oxygen relative to carbon and hydrogen were investigated quantitatively: radial transport of water ice-rich migrators across the snow line into the inner part of the solar nebula where the ice evaporates; and coagulation, vertical settling and evaporation of anhydrous dust in the median plane of the inner nebula. In both cases, the maximum achievable fO2, ~IW-4.5, produces a maximum XFa before diffusion ceases that is a factor of >7 less than would be required for UOC chondrule precursors, even for grains only 0.1 μm in radius and nebular cooling times as high as 106 yr. The same dynamic models are also incapable of creating environments sufficiently oxidizing to produce olivine with XFa = 0.15 during formation of chondrules by melting of FeO-poor precursors. If, instead, chondrule precursors were made of very FeO-rich, non-equilibrium condensates, reduction of chondrule melts by nebular gas may have been arrested before the mean XFa of chondrule olivine could fall below 0.15 because chondrules were hot for such a short time. A nebular origin for the mineral assemblage of unequilibrated enstatite chondrites (UECs) requires fO2 significantly below that of a system of solar composition. In particular, after fractionation of specific amounts of predicted high-temperature condensates, equilibrium condensation in a system whose Ptot = 10−4 atm and whose initial composition is solar except for a C/O ratio of 0.83 yields an assemblage characterized by a very large enstatite/forsterite ratio, the presence of oldhamite and niningerite, metallic nickel-iron containing several wt% Si, and small amounts of pure silica and albitic plagioclase, very similar to the mineral assemblage of EH3 chondrites. Log fO2 in this system varies from IW-8.9 at 1500 K to IW-13 at 900 K. The mechanisms proposed to date for fractionation of C, O and H from one another are quantitatively insufficient to produce the magnitude of nebular fO2 variations needed to account for primitive features of UOCs and UECs.