In order to explore the 4 \alpha-particle condensate state in 16O, we solve afull four-body equation of motion based on the 4 \alpha OCM (OrthogonalityCondition Model) in a large 4 \alpha model space spanned by Gaussian basisfunctions. A full spectrum up to the 0_6^+ state is reproduced consistentlywith the lowest six 0^+ states of the experimental spectrum. The 0^+_6 state isobtained at about 2 MeV above the 4 \alpha breakup threshold and has a dilutedensity structure, with a radius of about 5 fm. The state has an appreciablylarge \alpha condensate fraction of 61 %, and a large component of\alpha+12C(0_2^+) configuration, both features being reliable evidence for thisstate to be of 4 \alpha condensate nature.
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