We consider online mechanism design without money, where agents are allowed to trade items with other agents, in an attempt to improve their own allocation. In an off-line context, this problem is known as the House Allocation Problem (HAP). We extend HAP to an online problem and call it the Online House Allocation Problem (OHAP). In OHAP, agents can choose when to arrive and depart over time and are allowed to be indifferent between items. Subsequently, we present our Agent Shifting Algorithm (ASA) for OHAP. A mechanism that uses ASA as its allocation rule is shown to be strategy-proof, individually rational and Pareto optimal. Moreover, we argue that any mechanism that obtains an outcome in OHAP that cannot be obtained by using ASA fails to be strategy-proof or is not Pareto optimal.