The popularity of mobile devices and location-based services (LBSs) has raised significant concerns regarding the location privacy of their users. A popular approach to protect location privacy is anonymizing the users of LBS systems. In this paper, we introduce an information-theoretic notion for location privacy, which we call perfect location privacy. We then demonstrate how anonymization should be used by LBS systems to achieve the defined perfect location privacy. We study perfect location privacy under two models for user movements. First, we assume that a user's current location is independent from her past locations. Using this independent identically distributed (i.i.d.) model, we show that if the pseudonym of the user is changed before O(n2/r-1 ) observations are made by the adversary for that user, then the user has perfect location privacy. Here, n is the number of the users in the network and r is the number of all possible locations. Next, we model users' movements using Markov chains to better model real-world movement patterns. We show that perfect location privacy is achievable for a user if the user's pseudonym is changed before O(n 2/IEI-r observations are collected by the adversary for that user, where IEI is the number of edges in the user's Markov chain model.