The current standard of care for many patients with HER2-positive breast cancer is neoadjuvant chemotherapy in combination with anti-HER2 agents, based on HER2 amplification as detected by in situ hybridization (ISH) or protein immunohistochemistry (IHC). However, hematoxylin & eosin (H&E) tumor stains are more commonly available, and accurate prediction of HER2 status and anti-HER2 treatment response from H&E would reduce costs and increase the speed of treatment selection. Computational algorithms for H&E have been effective in predicting a variety of cancer features and clinical outcomes, including moderate success in predicting HER2 status. In this work, we present a novel convolutional neural network (CNN) approach able to predict HER2 status with increased accuracy over prior methods. We trained a CNN classifier on 188 H&E whole slide images (WSIs) manually annotated for tumor Regions of interest (ROIs) by our pathology team. Our classifier achieved an area under the curve (AUC) of 0.90 in cross-validation of slide-level HER2 status and 0.81 on an independent TCGA test set. Within slides, we observed strong agreement between pathologist annotated ROIs and blinded computational predictions of tumor regions / HER2 status. Moreover, we trained our classifier on pre-treatment samples from 187 HER2+ patients that subsequently received trastuzumab therapy. Our classifier achieved an AUC of 0.80 in a five-fold cross validation. Our work provides an H&E-based algorithm that can predict HER2 status and trastuzumab response in breast cancer at an accuracy that may benefit clinical evaluations.