As art historians have noted, "Les Demoiselles d'Avignon" (1907) occupies a very special place in the history of Western painting, both as the harbinger of 20th century modernism and as the progenitor of Cubism. For these reasons, as also for its convoluted history and multivariate interpretations, there is a vast art-historical literature on the painting. Yet creativity researchers have scarcely showed any interest in it as a creative phenomenon. This neglect is all the more striking once one realizes how the painting affords a veritable laboratory for exploring the nature of the "complexity" of creativity. Using the "cognitive-historical approach" this paper seeks to illuminate the complexity of the process by which "Les Demoiselles d'Avignon" came into being. In particular, it shows how the integrative actions of such cognitive processes as goal generation and structuring, purposive evolution, directed search through problem spaces, schema generation and elaboration, knowledge search, and cognitive identification, combined with elements of Picasso's cultural-historical milieu, and the knowledge-based interpretative judgment of later consumers of the painting shed light on the complexity of its creation.