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