Conversational Question Answering (CQA) systems meet user information needs by having conversations with them, where answers to the questions are retrieved from text. There exist a variety of datasets for English, with tens of thousands of training examples, and pre-trained language models have allowed to obtain impressive results. The goal of our research is to test the performance of CQA systems under low-resource conditions which are common for most non-English languages: small amounts of native annotations and other limitations linked to low resource languages, like lack of crowdworkers or smaller wikipedias. We focus on the Basque language, and present the first non-English CQA dataset and results. Our experiments show that it is possible to obtain good results with low amounts of native data thanks to cross-lingual transfer, with quality comparable to those obtained for English. We also discovered that dialogue history models are not directly transferable to another language, calling for further research. The dataset is publicly available.