All large, ground- and space-based astronomical facilities serving wide communities face a similar problem: in many cases the number of applications they receive in response to each call exceeds 1000. This poses a serious challenge to running an effective selection process under the classic peer-review paradigm, in which the proposals are assigned to pre-allocated panels with fixed compositions. Although, in principle, one could increase the size of the time allocation committee, this creates logistic and financial problems which place a practical limit on its maximum size, making this solution unviable beyond a certain volume of applications. For this reason, alternative solutions must be sought. One of these is the so-called Distributed Peer Review (DPR) in which, by submitting a proposal, the Principal Investigators (PIs) agree both to act as reviewers and to have their proposal reviewed by their peers. In this article we report the results of a DPR experiment run by ESO in Period 103, in parallel with the regular review by the Observing Programmes Committee (OPC).