Unsupervised domain adaptation (UDA) aims at learning a machine learning model using a labeled source domain that performs well on a similar yet different, unlabeled target domain. UDA is important in many applications such as medicine, where it is used to adapt risk scores across different patient cohorts. In this paper, we develop a novel framework for UDA of time series data, called CLUDA. Specifically, we propose a contrastive learning framework to learn contextual representations in multivariate time series, so that these preserve label information for the prediction task. In our framework, we further capture the variation in the contextual representations between source and target domain via a custom nearest-neighbor contrastive learning. To the best of our knowledge, ours is the first framework to learn domain-invariant, contextual representation for UDA of time series data. We evaluate our framework using a wide range of time series datasets to demonstrate its effectiveness and show that it achieves state-of-the-art performance for time series UDA.