Bird sound data collected with unattended microphones for automatic surveys, or mobile devices for citizen science, typically contain multiple simultaneously vocalizing birds of different species. However, few works have considered the multi-label structure in birdsong. We proposed to use an ensemble of classifier chains combined with binary relevance and three multi-instance multi-label learning (MIML) algorithms from prior work (which focus more on structure in sound, and less on structure in the label sets). Experiments are conducted on two real-world birdsong datasets, and show that the proposed method usually outperforms binary relevance (using the same features and base-classifier), and is better in some cases and worse in others compared to the MIML algorithms.