Annotation errors can significantly hurt classifier performance, yet datasets are only growing noisier with the increased use of Amazon Mechanical Turk and techniques like distant supervision that automatically generate labels. In this paper, we present a robust extension of logistic regression that incorporates the possibility of mislabelling directly into the objective. Our model can be trained through nearly the same means as logistic regression, and retains its efficiency on high-dimensional datasets. Through named entity recognition experiments, we demonstrate that our approach can provide a significant improvement over the standard model when annotation errors are present.