Many named entities contain other named entities inside them. Despite this fact, the field of named entity recognition has almost entirely ignored nested named entity recognition, but due to technological, rather than ideological reasons. In this paper, we present a new technique for recognizing nested named entities, by using a discriminative constituency parser. To train the model, we transform each sentence into a tree, with constituents for each named entity (and no other syntactic structure). We present results on both newspaper (...) and biomedical corpora which contain nested named entities. In three out of four sets of experiments, our model outperforms a standard semi-CRF on the more traditional top-level entities. At the same time, we improve the overall F-score by up to 30% over the flat model, which is unable to recover any nested entities. (shrink)