When a data set is partitioned, the resulting subsets may contain phylogenetically conflicting signals if they have different evolutionary histories. In a data set with many taxa, a single taxon that contains multiple phylogenetic histories may result in significant global incongruence, but no methods are available in a parsimony framework to localize incongruence to specific clades in a phylogeny and test the significance of incongruence on a local scale. Here we present a new method to quantify the conflict between data partitions for any clade in a phylogeny and to test the statistical significance of that conflict using a metric called the local incongruence length difference. We apply this method to the evolutionary history of the nuclear receptor superfamily, a large group of transcriptional regulators that play essential roles in metazoan development and physiology. All nuclear receptors are composed of several discrete domains, including one that binds to DNA response elements on specific target genes and another that binds to the appropriate ligand. We have performed combined and separate phylogenetic analyses of these two domains and have tested the hypothesis that nuclear receptors have evolved by a simple process of lineage splitting and divergence, without domain shuffling or other forms of sequence transfer between proteins. Our analysis indicates that significant conflict exists between the partitioned domains at a limited number of nodes on the tree, suggesting that several groups of receptors are "hybrid proteins" formed by domain shuffling or other forms of sequence transfer between more ancient nuclear receptors.