Early object name learning is often conceptualized as a problem of mapping heard names to referents. However, infants do not hear object names as discrete events but rather in extended interactions organized around goal-directed actions on objects. The present study examined the statistical structure of the "nonlinguistic" events that surround parent naming of objects. Parents and 12-month-old infants were left alone in a room for 10 minutes with 32 objects available for exploration. Parent and infant handling of objects and parent naming of objects were coded. The four measured statistics were from measures used in the study of coherent discourse: (i) a frequency distribution in which actions were frequently directed to a few objects and more rarely to other objects; (ii) repeated returns to the high-frequency objects over the 10-minute play period; (iii) clustered repetitions and continuity of actions on objects; and (iv) structured networks of transitions among objects in play that connected all the played-with objects. Parent naming was infrequent but related to the statistics of object-directed actions. The implications of the discourse-like stream of actions are discussed in terms of learning mechanisms that could support rapid learning of object names from relatively few name-object co-occurrences.