We report evidence for the simultaneous production of J/ψ and ϒ mesons in 8.1 fb^{-1} of data collected at sqrt[s]=1.96 TeV by the D0 experiment at the Fermilab pp[over ¯] Tevatron Collider. Events with these characteristics are expected to be produced predominantly by gluon-gluon interactions. In this analysis, we extract the effective cross section characterizing the initial parton spatial distribution, σ_{eff}=2.2±0.7(stat)±0.9(syst) mb.