Using proper motion data for 894 stars in the Orion Nebula Cluster (ONC) compiled by Jones & Walker in 1988, we search for binaries with apparent separations in the range 1000-5000 AU, and find an upper limit of three. Using a Monte Carlo method, we test the consistency of this result with two hypotheses: i) that the cluster contains a binary population identical to that found in the solar neighbourhood, and ii) that the cluster contains no binaries at all in this separation range. We obtain results strongly favouring the latter hypothesis. Star formation in the Galaxy is seen to occur in a variety of different environments, but it has been proposed that most stars may be formed in dense regions similar to the ONC, rather than in less dense groupings like that found in Taurus-Auriga. Since roughly 15 per cent of galactic field stars are known to be in binaries with separations greater than 1000 AU, the apparent absence of such binaries in the ONC places an upper limit on the contribution that dense clusters can make to galactic star formation.