Digital fingerprinting is used to trace back illegal users, where unique ID known as digital fingerprints is embedded into a content before distribution. On the generation of such fingerprints, one of the important properties is collusion-resistance. Binary codes for fingerprinting with a code length of theoretically minimum order were proposed by Tardos, and the related works mainly focused on the reduction of the code length were presented. In this paper, we present a concrete and systematic construction of the Tardos's fingerprinting code using a chaotic map. Using a statistical model for correlation scores, a proper threshold for detecting colluders is calculated. Furthermore, for the reduction of computational costs required for the detection, a hierarchical structure is introduced on the codewords. The collusion-resistance of the generated fingerprinting codes is evaluated by a computer simulation.