We study a natural generalization of the correlation clustering problem to graphs in which the pairwise relations between objects are categorical instead of binary. This problem was recently introduced by Bonchi et al. under the name of chromatic correlation clustering, and is motivated by many real-world applications in data-mining and social networks, including community detection, link classification, and entity de-duplication. Our main contribution is a fast and easy-to-implement constant approximation framework for the problem, which builds on a novel reduction of the problem to that of correlation clustering. This result significantly progresses the current state of knowledge for the problem, improving on a previous result that only guaranteed linear approximation in the input size. We complement the above result by developing a linear programming-based algorithm that achieves an improved approximation ratio of 4. Although this algorithm cannot be considered to be practical, it further extends our theoretical understanding of chromatic correlation clustering. We also present a fast heuristic algorithm that is motivated by real-life scenarios in which there is a groundtruth clustering that is obscured by noisy observations. We test our algorithms on both synthetic and real datasets, like social networks data. Our experiments reinforce the theoretical findings by demonstrating that our algorithms generally outperform previous approaches, both in terms of solution cost and reconstruction of an underlying ground-truth clustering.