Breast arterial calcifications (BACs) are part of several benign findings present on some mammograms. Previous studies have indicated that BAC may provide evidence of general atherosclerotic vascular disease, and potentially be a useful marker of cardiovascular disease (CVD). Currently, there is no technique in use for the automatic detection of BAC in mammograms. Since a majority of women over the age of 40 already undergo breast cancer screening with mammography, detecting BAC may offer a method to screen women for CVD in a way that is effective, efficient, and broad reaching, at no additional cost or radiation. In this paper, we present a deep learning approach for detecting BACs in mammograms. Inspired by the promising results achieved using the U-Net model in many biomedical segmentation problems and the DenseNet in semantic segmentation, we extend the U-Net model with dense connectivity to automatically detect BACs in mammograms. The presented model helps to facilitate the reuse of computation and improve the flow of gradients, leading to better accuracy and easier training of the model. We evaluate the performance using a set of full-field digital mammograms collected and prepared for this task from a publicly available dataset. Experimental results demonstrate that the presented model outperforms human experts as well as the other related deep learning models. This confirms the effectiveness of our model in the BACs detection task, which is a promising step in providing a cost-effective risk assessment tool for CVD.