In a search for evidence of evaporation during chondrule formation, the mesostases of 11 Bishunpur chondrules and melt inclusions in olivine phenocrysts in 7 of them have been analyzed for their alkali element abundances and K-isotopic compositions. Except for six points, all areas of the chondrules that were analyzed had δ41K compositions that were normal within error (typically ±3%, 2s̀). The six “anomalous” points are probably all artifacts. Experiments have shown that free evaporation of K leads to large 41K enrichments in the evaporation residues, consistent with Rayleigh fractionation. Under Rayleigh conditions, a 3% enrichment in δ41K is produced by ∼12% loss of K. The range of L-chondrite-normalized K/Al ratios (a measure of the K-elemental fractionation) in the areas analyzed vary by almost three orders of magnitude. If all chondrules started out with L-chondrite-like K abundances and the K loss occurred via Rayleigh fractionation, the most K-depleted chondrules would have had compositions of up to δ41K ≅ 200%. Clearly, K fractionation did not occur by evaporation under Rayleigh conditions. Yet experiments and modeling indicate that K should have been lost during chondrule formation under currently accepted formation conditions (peak temperature, cooling rate, etc.). Invoking precursors with variable alkali abundances to produce the range of K/Al fractionation in chondrules does not explain the K-isotopic data because any K that was present should still have experienced sufficient loss during melting for there to have been a measurable isotopic fractionation. If K loss and isotopic fractionation was inevitable during chondrule formation, the absence of K-isotopic fractionation in Bishunpur chondrules requires that they exchanged K with an isotopically normal reservoir during or after formation. There is evidence for alkali exchange between chondrules and rim-matrix in all unequilibrated ordinary chondrites. However, melt inclusions can have alkali abundances that are much lower than the mesostases of the host chondrules, which suggests that they at least remained closed since formation. If it is correct that some or all melt inclusions remained closed since formation, the absence of K-isotopic fractionation in them requires that the K-isotopic exchange took place during chondrule formation, which would probably require gas-chondrule exchange. Potassium evaporated from fine-grained dust and chondrules during chondrule formation may have produced sufficient K-vapor pressure for gas-chondrule isotopic exchange to be complete on the timescales of chondrule formation. Alternatively, our understanding of chondrule formation conditions based on synthesis experiments needs some reevaluation.