We consider an individual decision-making problem where the decision maker is subject to inattention. The source of this inattention is the frames with which the alternatives appear; leading to randomness in choice. We characterize a rule called frame-based stochastic choice rule, according to which the choice probability of an alternative (say, x) is the probability with which attention is drawn by its frame and not by the frames which are associated with the alternatives that beat x according to a complete and antisymmetric binary relation. The choice probability is zero if a better alternative appears with the same frame. The rule and the treatment are largely influenced by Manzini and Mariotti (2014). Our framework is applicable to settings where frames are advertisements or types of packaging.