We present Poisson Binomial Mechanism Vertical Federated Learning (PBM-VFL), a communication-efficient Vertical Federated Learning algorithm with Differential Privacy guarantees. PBM-VFL combines Secure Multi-Party Computation with the recently introduced Poisson Binomial Mechanism to protect parties' private datasets during model training. We define the novel concept of feature privacy and analyze end-to-end feature and sample privacy of our algorithm. We compare sample privacy loss in VFL with privacy loss in HFL. We also provide the first theoretical characterization of the relationship between privacy budget, convergence error, and communication cost in differentially-private VFL. Finally, we empirically show that our model performs well with high levels of privacy.