In a recent measurement LHCb reported pronounced structures in the J/ψJ/ψ spectrum.One of the var-ious possible explanations of those is that they emerge from non-perturbative interactions of vector char-monia.It is thus important to understand whether it is possible to form a bound state of two charmonia interacting through the exchange of gluons,which hadronise into two pions at the longest distance.In this paper,we demonstrate that,given our current understanding of hadron-hadron interactions,the exchange of correlated light mesons (pions and kaons) is able to provide sizeable attraction to the di-J/ψ system,and it is possible for two J/ψ mesons to form a bound state.As a side result we find from an analysis of the data for the ψ(2S) →J/ψππ transition including both ππ and K(K) final state interactions an improved value for the ψ(2S)→J/ψ transition chromo-electric polarisability:|αψ(2S)J/ψ| =(1.8 ±0.1)GeV-3,where the uncertainty also includes the one induced by the final state interactions.