Despite broad utility of time series data in industry, the data scarcity limits the application of machine learning approaches in this domain. In this work, we propose CCATS, a novel generative model to tackle this issue by generating synthetic class-conditional time series data, which can be used to augment existing data. As time series are so divers and dependent on their specific application, it is difficult to compose models that work for a broad spectrum of applications. As a result, many focus on a single, specific dataset for a specific application. This makes the comparison of different methods difficult and there is a lack of published work regarding conditional generative models on time series data more generally. In this paper, we adopt a U-Net architecture to build a diffusion model for time series generation and evaluate it on the UCR classification archive, which contains time series datasets of a great variety. We set a baseline on these datasets and probe the benefits of class-conditional time series generation. We confirm the training stability advantages over generative adversarial networks and significant improvements over a recent variational autoencoder approach, TimeVQVAE. We further test whether classifier-free guidance yields advantages over a model without additional guidance, and even find advantages over real data for some datasets.