Location-based sharing services allow people to connect with others who are near them, or with whom they shared a past encounter. Suppose it were also possible to connect with people who were at the same location but at a different time -- we define this scenario as a close encounter, i.e., an incident of spatial and temporal proximity. By detecting close encounters, a person infected with a contagious disease could alert others to whom they may have spread the virus. We designed a smartphone-based system that allows people infected with a contagious virus to send alerts to other users who may have been exposed to the same virus due to a close encounter. We address three challenges: finding devices in close encounters with minimal changes to existing infrastructure, ensuring authenticity of alerts, and protecting privacy of all users. Finally, we also consider the challenges of a real-world deployment.