While gazetteers can be used to perform named entity recognition through lookup-based methods, ambiguity and incomplete gazetteers lead to relatively low recall. A sequence model which uses more general features can achieve higher recall while maintaining reasonable precision, but typically requires expensive annotated training data. To circumvent the need for such training data, we bootstrap the learning of a sequence model with a gazetteer-driven labeling algorithm which only labels tokens in unlabeled data that it can label confidently. We present an algorithm, called the Partial Perceptron, for discriminatively learning the parameters of a sequence model from such partially labeled data. The algorithm is easy to implement and trains much more quickly than a state-of-the-art algorithm based on Conditional Random Fields with equivalent performance. Experimental results show that the learned model yields a substantial relative improvement in recall (77.3%) with some loss in precision (a 28.7% relative decrease) when compared to the gazetteer-driven method.