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We propose a trial wave function for the quantum Hall bilayer system of total filling factor ν_T=1 at a layer distance d to magnetic length ℓ ratio d/ℓ=κ_c1≈1.1, where the lowest charged excitation is known to have a level crossing. The wave function has two-particle correlations which fit well with those in previous numerical studies, and can be viewed as a Bose-Einstein condensate of free excitons formed by composite bosons and anti-composite bosons in different layers. We show the freedoi:10.1103/physrevlett.120.077601 pmid:29542942 fatcat:r6ufi7clnbctberr6qugot6ah4