Autonomous vehicle (AV) technology holds great promise for improving the efficiency of traditional vehicle sharing systems. In this paper, we investigate a new vehicle sharing system using AVs, referred to as autonomous vehicle sharing and reservation (AVSR). In such a system, travelers can request AV trips ahead of time and the AVSR system operator will optimally arrange AV pickup and delivery schedules and AV trip chains based on these requests. A linear programming model is proposed to efficiently solve for optimal solutions for AV trip chains and required fleet size through constructed AVSR networks. Case studies show that AVSR can significantly increase vehicle use rate (VUR) and consequentially reduce vehicle ownership significantly. In the meantime, it is found that the actual vehicle miles traveled (VMT) in AVSR systems is not significantly more than that of conventional taxis, despite inevitable empty hauls for vehicle relocation in AVSR systems. The results imply huge potential benefits from AVSR systems on improving mobility and sustainability of our current transportation systems.