Estimating potential outcomes for treatments over time based on observational data is important for personalized decision-making in medicine. Yet, existing neural methods for this task suffer from either (a) bias or (b) large variance. In order to address both limitations, we introduce the G-transformer (GT). Our GT is a novel, neural end-to-end model designed for unbiased, low-variance estimation of conditional average potential outcomes (CAPOs) over time. Specifically, our GT is the first neural model to perform regression-based iterative G-computation for CAPOs in the time-varying setting. We evaluate the effectiveness of our GT across various experiments. In sum, this work represents a significant step towards personalized decision-making from electronic health records.