Devices such as mobile phones, tablets, and sensors are often equipped with GPS that accurately report a person's location. Combined with wireless communication, these devices enable a wide range of new social tools and applications. These same qualities, however, leave location-aware applications vulnerable to privacy violations. This paper introduces the Negative Quad Tree, a privacy protection method for location aware applications. The method is broadly applicable to applications that use spatial density information, such as social applications that measure the popularity of social venues. The method employs a simple anonymization algorithm running on mobile devices, and a more complex reconstruction algorithm on a central server. This strategy is well suited to low-powered mobile devices. The paper analyzes the accuracy of the reconstruction method in a variety of simulated and real-world settings and demonstrates that the method is accurate enough to be used in many realworld scenarios.