Multi-label classification is a type of supervised machine learning that can simultaneously assign multiple labels to an instance. To solve this task, some methods divide the original problem into several sub-problems (local approach), others learn all labels at once (global approach), and others combine several classifiers (ensemble approach). Regardless of the approach used, exploring and learning label correlations is important to improve the classifier predictions. Ensemble of Classifier Chains (ECC) is a well-known multi-label method that considers label correlations and can achieve good overall performance on several multi-label datasets and evaluation measures. However, one of the challenges when working with ECC is the high dimensionality of the label space, which can impose limitations for fully-cascaded chains as the complexity increases regarding feature space expansion. To improve classifier chains, we propose a method to chain disjoint correlated label clusters obtained by applying a partition method in the label space. During the training phase, the ground truth labels of each cluster are used as new features for all of the following clusters. During the test phase, the predicted labels of clusters are used as new features for all the following clusters. Our proposal, called Label Cluster Chains for Multi-Label Classification (LCC-ML), uses multi-label Random Forests as base classifiers in each cluster, combining their predictions to obtain a final multi-label classification. Our proposal obtained better results compared to the original ECC. This shows that learning and chaining disjoint correlated label clusters can better explore and learn label correlations.