The properties of the inflation process and especially possible changes in its persistence have received much attention in the literature. However, empirical evidence is ambiguous. Some studies find that inflation persistence varied over time, others conclude it was constant. This article contributes further evidence to this ongoing debate by modeling U.S. inflation dynamics using a sticky infinite hidden Markov model (sticky IHMM). The sticky IHMM is a Bayesian nonparametric approach to modeling structural breaks. It allows for an unknown number of breakpoints and is a flexible and attractive alternative to existing methods. We found that inflation persistence was highest in 1973-74 and then again around 1980. However, credible intervals for our estimates of inflation persistence were very wide. Thus, a substantial amount of uncertainty about this aspect of inflation dynamics remained.