The frequency of errors during genome replication limits the amount of functionally important information that can be passed on from generation to generation. During the origin of life, mutation rates are thought to have been quite high, raising a classic chicken-and-egg paradox: could nonenzymatic replication propagate sequences accurately enough to allow for the emergence of heritable function? Here we show that the theoretical limit on genomic information content may increase substantially as a consequence of dramatically slowed polymerization after mismatches. As a result of postmismatch stalling, accurate copies of a template tend to be completed more rapidly than mutant copies and the accurate copies can therefore begin a second round of replication more quickly. To quantify this effect, we characterized an experimental model of nonenzymatic, template-directed nucleic acid polymerization. We found that most mismatches decrease the rate of primer extension by more than 2 orders of magnitude relative to a matched (Watson-Crick) control. A chemical replication system with this property would be able to propagate sequences long enough to have function. Our study suggests that the emergence of functional sequences during the origin of life would be possible even in the face of the high intrinsic error rates of chemical replication.