Accountable Care Organizations (ACOs) are new organizations created by the Affordable Care Act to encourage more efficient, integrated care delivery. To promote efficiency, ACOs sign contracts under which they keep a fraction of the savings from keeping costs below target provided they also maintain quality levels. To promote integration and facilitate measurement, ACOs are required to have at least 5000 enrollees and so must coordinate across many providers. We calibrate a model of optimal ACO incentives using proprietary performance measures from a large insurer. Our key finding is that free-riding is a severe problem and causes optimal incentive payments to exceed cost savings unless ACOs simultaneously achieve extremely large efficiency gains. This implies that successful ACOs will likely rely on motivational strategies that amplify the effects of under-powered incentives. These motivational strategies raise important questions about the limits of ACOs as a policy for promoting more efficient, integrated care (JEL D23, D86, I12, L14, L24, M52).