Here we describe a new clinical corpus rich in nested entities and a series of neural models to identify them. The corpus comprises de-identified referrals from the waiting list in Chilean public hospitals. A subset of 5,000 referrals (58.6% medical and 41.4% dental) was manually annotated with 10 types of entities, six attributes, and pairs of relations with clinical relevance. In total, there are 110,771 annotated tokens. A trained medical doctor or dentist annotated these referrals, and then, together with three other researchers, consolidated each of the annotations. The annotated corpus has 48.17% of entities embedded in other entities or containing another one. We use this corpus to build models for Named Entity Recognition (NER). The best results were achieved using a Multiple Single-entity architecture with clinical word embeddings stacked with character and Flair contextual embeddings. The entity with the best performance is abbreviation, and the hardest to recognize is finding. NER models applied to this corpus can leverage statistics of diseases and pending procedures. This work constitutes the first annotated corpus using clinical narratives from Chile and one of the few in Spanish. The annotated corpus, clinical word embeddings, annotation guidelines, and neural models are freely released to the community.