Students preparing for software engineering careers need to be proficient in the mechanics of communication and experienced in the basic communication genres common to the profession. We argue, however, that this is not enough: students must also be prepared for the inventive, in-the-moment nature of real project communication. Choosing the right moment and manner for inventive discourse is the essence of kairos, a long-standing concept in the field of rhetoric. We find similarities between the concept of kairos and the role of communication in agile software development methods. We argue for the need to address kairos in software engineering education. We present an approach, based on the concept of cognitive apprenticeship, that we have used in a team software project course with successful results. Finally, we pose two important challenges: how to evaluate kairotic awareness across a student's academic career and beyond, and how to make software engineering instructors feel comfortable covering communication topics.