The present invention relates to a monomodal coupled diene elastomer having a silanol functional group in the middle of the chain, to its process of preparation and to a rubber composition which can be used in particular in the manufacture of tyre covers, having improved hysteresis and physical properties in the vulcanized state and an improved processing in the raw state, comprising a monomodal diene polymer having a silanol functional group in the middle of the chain and a reinforcing inorganic filler.The process for obtaining this elastomer having a silanol functional group in the middle of the chain comprises a reaction of the diene monomer(s) and of the polymerization initiator in the presence of a chelating polar agent, a reaction of the living diene polymer with a coupling agent and then, after hydrolysis, a recovery of the coupled diene polymer having a functional group in the middle of the chain.A rubber composition according to the invention comprises a reinforcing inorganic filler and this monomodal elastomer having a silanol functional group in the middle of the chain.