Chromatic Correlation Clustering (CCC) (introduced by Bonchi et al. ) is a natural generalization of the celebrated Correlation Clustering (CC) problem, introduced by Bonchi et al. . It models objects with categorical pairwise relationships by an edge-colored graph, and has many applications in data mining, social networks and bioinformatics. We show that there exists a $2.5$-approximation to the CCC problem based on a Linear Programming (LP) approach, thus improving the best-known approximation ratio of 3 achieved by Klodt et al.  . We also present an efficient heuristic algorithm for CCC leveraging a greedy clustering strategy, and conduct extensive experiments to demonstrate the effectiveness and efficiency of our proposed algorithm.