This paper illustrates how one can deduce preference from observed choices when attention is not only limited but also random. In contrast to earlier approaches, we introduce a Random Attention Model (RAM) where we abstain from any particular attention formation, and instead consider a large class of nonparametric random attention rules. Our model imposes one intuitive condition, termed Monotonic Attention, which captures the idea that each consideration set competes for the decision-maker's attention. We then develop revealed preference theory within RAM and obtain precise testable implications for observable choice probabilities. Based on these theoretical findings, we propose econometric methods for identification, estimation, and inference of the decision maker's preferences. To illustrate the applicability of our results and their concrete empirical content in specific settings, we also develop revealed preference theory and accompanying econometric methods under additional nonparametric assumptions on the consideration set for binary choice problems. Finally, we provide general purpose software implementation of our estimation and inference results, and showcase their performance using simulations.