A secure location-based service requires that a mobile user certifies his position before gaining access to a resource. Currently, most of the existing solutions addressing this issue assume a trusted third party that can vouch for the position claimed by a user. However, as computation and communication capacities become ubiquitous with the large scale adoption of smartphones by individuals, we propose to leverage on these resources to solve this issue in a collaborative and private manner. More precisely, we introduce PROPS, for PRivacy-preserving lOcation Proof System, which allows users to generate proofs of location in a private and distributed way using neighboring nodes as witnesses. PROPS provides security properties such as unforgeability and non-transferability of the proofs, as well as resistance to classical localization attacks.