The paper consists of four chapters. The first one contains an overview of the earliest extant forms of historical writing in Kievan Rus. These include: letopisi (annalistic chronicles, including the Primary Chronicle, or Povest vremennykh let, of the 1110s), translations of Byzantine chronicles and compendia (khronographs) based on them (the latter, perhaps, do not belongto the earliest forms of historiogpraphy), the mid-eleventh-century Sermon on Law and Grace of Metropolitan Hilarion (which includes historical reflections), the quasi-annalistic notes on Saint Vladimir in one of his early lives by Jacob the Monk, the historical graffiti on the walls of the churches (the earliest ones date from the mid-eleventh century), the Novgorodian lists of princes and bishops (probably based on proto-lists of the 1090s), and some other minor forms of historical records. The second chapter is an overview of the hypotheses expressed by scholars on the beginnings of historical writing in Rus. The most discussed one is the hypothesis of the so-called Earliest Tale, or narrative (non-annalistic) nucleus of the Primary Chronicle. The hypothesis as such is convincing, but the date and the exact limits of this text are subject to debate and still problematic. This early narration could be created in Saint Vladimirs time, early in the eleventh century, but more probably in the time of Yaroslav the Wise (1016-1054) or even later. Another idea (and again very convincing one) is that of brief annals kept in Kiev during the first half of the eleventh century. These annals later, in the second half of the same century, were combined with the narrative nucleus and gave birth to annalistic chronicles as we know them. Some other ideas on the form of the earliest historical records in Rus also are reviewed, including the likely hypothesis that Jacob the Monks quasi-annals reflect a very early brief description of Vladimirs reign. The view at the Primary Chronicle of the 1110s as the earliest extended historical work in Rus is criticized. The third chapter is dedicated to a comparative approach to the problem. One can find parallels to any of the early Rus historical writings but the problem is what the earliest, non-extant ones looked like. In ancient societies (Sumer, Egypt, China), where writing had developed independently and was not imported (as in Rus), brief records (such as royal inscriptions, annals of liturgical significance, king-lists, etc.) preceded comprehensive historiographical works for centuries or even millenia. But when we look at societies which (as Rus) received writing with conversion (Anglo-Saxon kingdoms, Poland, the Czechs, partly Scandinavia) we find an opposite picture: in these countries there were extended historical narrations which aimed to place a newly converted country and its dynastic past into the history of the world. The hypothetical Earliest Tale fits well this tendency. But in the countries mentioned the chronological distance between the conversion and the creation of such a historiographical work was not less than 100 years. Thus, it seems that the Earliest Tale must be dated later than Vladimirs reign to allow some chronological distance between it and the conversion of Rus in 988. The comparative material shows also that it is very probable that there were some early brief forms of historical writing, such as annals, lists of princely deeds etc. The absence of early written genealogies in Rus is, however, striking. The fourth chapter contains conclusions. The beginnings of historical writing in Rus are still obscure, but one can be more or less sure that the first texts were, on the one hand, a coherent narrative on the early history of Rus and, on the other hand, brief annals. This time was an important period in the formation of the state in Rus when the court istitutionalized and written laws appeared. The question of the status of the first historical writing as well of the role of influences from abroad also are discussed.