Out-of-distribution (OOD) detection is critical when deploying machine learning models in the real world. Outlier exposure (OE) methods, which incorporate auxiliary outlier data (AUX) in the training process, can drastically improve OOD detection performance. We introduce Hopfield Boosting, a boosting approach, which leverages modern Hopfield energy to sharpen the decision boundary between the in-distribution (ID) and OOD data. Hopfield Boosting encourages the model to focus on hard-to-distinguish auxiliary outlier examples that lie close to the decision boundary between ID and AUX data. Our method achieves a new state-of-the-art in OOD detection with OE, improving the FPR95 from 2.28 to 0.92 on CIFAR-10, from 11.24 to 7.94 on CIFAR-100, and from 50.74 to 36.60 on ImageNet-1K.