We report high precision (+/-0.5 parts per thousand) potassium isotopic determinations on bulk chondrites, achondrites, and lunar samples, on a separated chondrule, and two CAIs. We find that potassium shows a remarkable isotopic homogeneity in various solar system bodies, even though there are chemical depletions of a factor of about 30, between C1 chondrites and eucrites and lunar samples. Theories that propose the evaporation of volatile elements from initially condensed (C1 chondrite) material to account for such chemical depletions, necessarily imply the existence of large isotopic mass fractionations, e.g., about +40 parts per thousand for Earth, +90 parts per thousand for eucrites and lunar rocks. Volatile loss of potassium (and by implication Na, Rb, Cs, and other elements of similar volatility) during chondrule formation is also ruled out. The high precision of the data place stringent limits of less than or equal to 2% on the quantity of potassium that could have been lost by partial volatilization. This is not detectable by standard chemical techniques, which can resolve 5-20% changes in the K/La and K/U ratios. The two-component models proposed by Larimer and Anders (1967) and by Wanke et al. (1984) invoke vaporization of alkalis which is not supported by the potassium isotope results. The chemical depletion of alkalis and other volatiles must have preceded the processes of chondrule, chondrite, and planetary formation, and occurred during the condensation of precursor dust, probably from a hot stage in the solar nebula.