Levelized costs of electricity (LCOE) are a common metric for comparing power generating technologies. However, there is qualified criticism particularly towards evaluating variable renewables like wind and solar power based on LCOE because it ignores integration costs that occur at the system level. In this paper we propose a new measure System LCOE as the sum of generation and integration costs per unit of VRE. For this purpose we develop a conclusive definition of integration costs. Furthermore we decompose integration costs into different cost components and draw conclusions for integration options like transmission grids and energy storage. System LCOE are quantified from a power system model and a literature review. We find that at moderate wind shares (~20%) integration costs can be in the same range as generation costs of wind power and conventional plants. Integration costs further increase with growing wind shares. We conclude that integration costs can become an economic barrier to deploying VRE at high shares. This implies that an economic evaluation of VRE must not neglect integration costs. A pure LCOE comparison would significantly underestimate the costs of VRE at high shares. System LCOE give a framework of how to consistently account for integration costs and thus guide policy makers and system planers in designing a cost-efficient power system.