We report on a search for B0↔B0 oscillations (mixing) using events with two identified muons from data collected at the CERN pp collider. In the absence of B0↔B0 oscillations, dimuons coming directly from decays of beauty-antibeauty paris must have opposite signs. Like-sign dimuons are expected from events where one muon arises from beauty decay and the other from the charm decay of the associated beauty-charm cascade. Taking these processes into account, together with the contribution from charm production, the predicted ratio of like-sign to unlike-sign muon pairs is 0.26±0.03. Experimentally we measure 0.42±0.07±0.03. A natural explanation for the excess of like-sign events is the existence of a significant amount of B0↔B0 transitions. The fraction of beauty particles that produce first-generation decay muons with the opposite electric charge from that expected without mixing is deduced to be: χ = 0.121±0.047. Combined with the null result from searches for B0↔B0 oscillations at e+e- colliders, our results are consistent with transitions inthe B0s system, as favoured theoretically.