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The chronology of dust formation in the early solar system remains controversial. Chondrules are the most abundant high-temperature objects formed during the evolution of the circumsolar disk. Considering chondrule formation, absolute lead‑lead (PbPb) ages and aluminum‑magnesium (26Al26Mg) ages relative to calcium‑aluminum-rich inclusions (CAIs) provide inconsistent chronologies, with PbPb ages showing early and protracted chondrule formation episodes whereas 26Al26Mg ages suggest that chondrule production was delayed by >1.5 Ma. Here, we develop a new method to precisely determine in situ 26Al26Mg ages of spinel-bearing chondrules, which are not affected by secondary asteroidal processes. Our data demonstrate that 26Al26Mg chondrule formation ages are actually 1 Ma older than previously thought and extend over the entire lifetime of the disk. This shift in chondrule formation ages relative to CAIs, however, is not sufficient to reconcile the PbPb and 26Al26Mg chronologies of chondrule and achondrite formation. Thus, either chondrules' PbPb ages and volcanic achondrites' 26Al26Mg ages are incorrect or the age of CAIs should be reevaluated at 4,568.7 Ma to ensure consistency between chronometers. We favor the second hypothesis, given that (i) the canonical age of CAIs was determined using only 4 specimens and (ii) older ages of 4,568.2 Ma have also been measured. We show that the adoption of 4,568.7 Ma as the new canonical age of CAIs and the use of our new spinel-derived 26Al26Mg ages enable reconciling the PbPb and 26Al26Mg ages of chondrules and achondrites. This new chronology implies the existence of a 0.7–1 Ma gap between the formation of refractory inclusions and chondrules, and supports the homogeneous distribution of 26Al in the circumsolar disk.