Differentially private stochastic gradient descent (DPSGD) is a variation of stochastic gradient descent based on the Differential Privacy (DP) paradigm, which can mitigate privacy threats that arise from the presence of sensitive information in training data. However, one major drawback of training deep neural networks with DPSGD is a reduction in the models accuracy. In this paper, we study the effect of normalization layers on the performance of DPSGD. We demonstrate that normalization layers significantly impact the utility of deep neural networks with noisy parameters and should be considered essential ingredients of training with DPSGD. In particular, we propose a novel method for integrating batch normalization with DPSGD without incurring an additional privacy loss. With our approach, we are able to train deeper networks and achieve a better utility-privacy trade-off.