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Blood oxygen level dependent (BOLD) MRI with maternal hyperoxia can assess oxygen transport within the placenta and has emerged as a promising tool to study placental function. Measuring signal changes over time requires segmenting the placenta in each volume of the time series. Due to the large number of volumes in the BOLD time series, existing studies rely on registration to map all volumes to a manually segmented template. As the placenta can undergo large deformation due to fetal motion, maternal motion, and contractions, this approach often results in a large number of discarded volumes, where the registration approach fails. In this work, we propose a machine learning model based on a U-Net neural network architecture to automatically segment the placenta in BOLD MRI and apply it to segmenting each volume in a time series. We use a boundary-weighted loss function to accurately capture the placental shape. Our model is trained and tested on a cohort of 91 subjects containing healthy fetuses, fetuses with fetal growth restriction, and mothers with high BMI. We achieve a Dice score of 0.83+/-0.04 when matching with ground truth labels and our model performs reliably in segmenting volumes in both normoxic and hyperoxic points in the BOLD time series. Our code and trained model are available at https://github.com/mabulnaga/automatic-placenta-segmentation.