This paper illustrates how one can deduce preference from observed choices when attention is both limited and random. We introduce a random attention model where we abstain from any particular attention formation and instead consider a large class of nonparametric random attention rules. Our intuitive condition, monotonic attention, captures the idea that each consideration set competes for the decision maker’s attention. We then develop a revealed preference theory and obtain testable implications. We propose econometric methods for identification, estimation, and inference for the revealed preferences. Finally, we provide a general-purpose software implementation of our estimation and inference results and simulation evidence.