The topic of big data has attracted increasing interest in recent years. The emergence of big data leads to new difficulties in terms of protection models used for data privacy, which is of necessity for sharing and processing data. Protecting individuals' sensitive information while maintaining the usability of the data set published is the most important challenge in privacy preserving. In this regard, data anonymization methods are utilized in order to protect data against identity disclosure and linking attacks. In this study, a novel data anonymization algorithm based on chaos and perturbation has been proposed for privacy and utility preserving in big data. The performance of the proposed algorithm is evaluated in terms of Kullback-Leibler divergence, probabilistic anonymity, classification accuracy, F-measure and execution time. The experimental results have shown that the proposed algorithm is efficient and performs better in terms of Kullback-Leibler divergence, classification accuracy and F-measure compared to most of the existing algorithms using the same data set. Resulting from applying chaos to perturb data, such successful algorithm is promising to be used in privacy preserving data mining and data publishing.