In this work, we present the Grounded Recurrent Neural Network (GRNN), a recurrent neural network architecture for multi-label prediction which explicitly ties labels to specific dimensions of the recurrent hidden state (we call this process "grounding"). The approach is particularly well-suited for extracting large numbers of concepts from text. We apply the new model to address an important problem in healthcare of understanding what medical concepts are discussed in clinical text. Using a publicly available dataset derived from Intensive Care Units, we learn to label a patient's diagnoses and procedures from their discharge summary. Our evaluation shows a clear advantage to using our proposed architecture over a variety of strong baselines.