Aggregating multiple access interfaces of a client is a promising way to satisfy the high bandwidth demand by high-definition video streaming services. However, how to efficiently use such aggregated bandwidth to improve the reliability of timely fetching video contents needs to be further studied. In this paper, we propose a partial overlapping chunk based dual-path transmission scheme, which uses partial redundancy based transmissions to optimize the playback performance at the client side. Specifically, we schedule the transmissions of different sized chunks with partial overlapping according to the delivery capabilities of different paths. We then build an optimal model to compute the optimal overlapping ratio between the transmitted chunks to maximize the probability of timely fetching of video contents. Numerical results demonstrate that, our scheme can improve the probability of timely fetching video contents, by up to 19.3%, compared to the traditional scheme without chunk overlapping, while the incurred average transmission redundancy is below 14.4%.