Chondrules and Ca-Al-rich inclusions (CAIs) are high-temperature components of meteorites that formed during transient heating events in the early Solar System. A major unresolved issue is the relative timing of CAI and chondrule formation. From the presence of chondrule fragments in an igneous CAI, it was concluded that some chondrules formed before CAIs (ref. 5). This conclusion is contrary to the presence of relict CAIs inside chondrules, as well as to the higher abundance of 26Al in CAIs; both observations indicate that CAIs pre-date chondrules by 1-3 million years (Myr). Here we report that relict chondrule material in the Allende meteorite, composed of olivine and low-calcium pyroxene, occurs in the outer portions of two CAIs and is 16O-poor (Delta17O approximately -1 per thousand to -5 per thousand). Spinel and diopside in the CAI cores are 16O-rich (Delta17O up to -20 per thousand), whereas diopside in their outer zones, as well as melilite and anorthite, are 16O-depleted (Delta17O = -8 per thousand to 2 per thousand). Both chondrule-bearing CAIs are 26Al-poor with initial 26Al/27Al ratios of (4.7 +/- 1.4) x 10(-6) and <1.2 x 10(-6). We conclude that these CAIs had chondrule material added to them during a re-melting episode approximately 2 Myr after formation of CAIs with the canonical 26Al/27Al ratio of 5 x 10(-5).