The automatic detection of anomalies in communication networks plays a central role in network management. Despite the many attempts and approaches for anomaly detection explored in the past, the detection of rare events in multidimensional network data streams still represents a complex to tackle problem. Network monitoring data generally consists of hundreds of counters periodically collected in the form of time-series, resulting in a complex-toanalyze multivariate time-series (MTS) process. Traditional timeseries anomaly detection methods target univariate time-series analysis, which makes the multivariate analysis cumbersome and prohibitively complex when dealing with MTS data. In this paper we introduce DC-VAE, a novel approach to anomaly detection in MTS data, leveraging convolutional neural networks (CNNs) and variational auto encoders (VAEs). DC-VAE detects anomalies in MTS data through a single model, exploiting temporal information without sacrificing computational and memory resources. In particular, instead of using recursive neural networks, large causal filters, or many layers, DC-VAE relies on Dilated Convolutions (DC) to capture long and short term phenomena in the data, avoiding complex and less-efficient deep architectures, thus simplifying learning. We evaluate DC-VAE on the detection of anomalies in the TELCO dataset, a large-scale, multi-dimensional network monitoring dataset collected at an operational mobile Internet Service Provider (ISP), where anomalous events were manually labeled by experts during a time span of seven-months, at a five-minutes granularity. Results show the main properties and advantages introduced by VAEs for time-series anomaly detection, as well as the out-performance of DC-VAE as compared to standard VAEs for time-series modeling. We also evaluate DC-VAE in open, publicly available datasets, comparing its performance against other multivariate anomaly detectors based on deep learning generative models. For the sake of reproducibility and as an additional contribution, we make the TELCO dataset publicly available to the community, and openly release the code implementing DC-VAE.