Most commercial video streaming systems rely on Content Distribution Networks (CDNs) to distribute video content. HTTP adaptive streaming has been recently adopted by major video streaming providers and is now considered the standard technique used with CDN-based streaming systems. Despite the success of these systems, cost-effective scalability continues to be of concern in their design and deployment. To address this, recent work has proposed the use of hybrid CDN and Peer-to-peer (P2P) live streaming systems. The design of these systems aims to combine the scalability of P2P systems and the desirable performance properties of CDN-based systems. However, the use of adaptive streaming, has not been explored extensively in such hybrid systems. Designing and operating an adaptive hybrid streaming system is very challenging. Two design decisions are very critical in the operation of any such system. The first one is the bitrate adaptation strategy which specifies how different bitrates are assigned to different users while maximizing user satisfaction. The second is defining the operational guidelines for switching the system between the CDN and the P2P modes while efficiently utilizing the available resources. In this paper we present a model and analysis of a hybrid CDN-P2P adaptive live streaming system with the objective of answering these two design questions. We first present a stochastic fluid model to the hybrid streaming system with a single video bitrate and we obtain theoretical results to guide the system operation as described above. We then extend the analysis to the adaptive streaming case with multiple video bitrates. We model adaptive streaming as a linear optimization problem to obtain the best bitrate adaptation strategy. We validate our analysis using simulations. Our conclusion is that adaptive hybrid streaming can significantly improve the ability of the system to satisfy more users with higher video bitrates over CDN-based systems.