Prices tend to remain constant for a period of time and then jump. In the literature, this "rigidity" is usually interpreted to reflect a cost of adjusting prices. This article shows that price rigidity can alternatively reflect optimal price setting when there are no adjustment costs, namely, if the seller is rationally inattentive. The model generates non-trivial pricing patterns that are consistent with the data and that are hard to explain with the traditional adjustment-cost model. In particular, prices are adjusted frequently but move back and forth between a few given values, hazard functions are downward sloping, and responses to persistent shocks are sluggish. These results are obtained in a model that implements rational inattention without simplifying assumptions on the functional forms of the processed signals.