  We report ALMA observations in 0.87 mm continuum and $^{12}$CO ($J$ = 3--2)
toward a very low-luminosity ($<$0.1 $L_{\odot}$) protostar, which is deeply
embedded in one of the densest core MC27/L1521F, in Taurus with an indication
of multiple star formation in a highly dynamical environment. The beam size
corresponds to $\sim$20 AU, and we have clearly detected blueshifted/redshifted
gas in $^{12}$CO associated with the protostar. The spatial/velocity
distributions of the gas show there is a rotating disk with a size scale of
$\sim$10 AU, a disk mass of $\sim$10$^{-4}$ $M_{\odot}$ and a central stellar
mass of $\sim$0.2 $M_{\odot}$. The observed disk seems to be detached from the
surrounding dense gas, although it is still embedded at the center of the core
whose density is $\sim$10$^{6}$ cm$^{-3}$. The current low-outflow activity and
the very low luminosity indicate that the mass accretion rate onto the
protostar is extremely low in spite of a very early stage of star formation. We
may be witnessing the final stage of the formation of $\sim$0.2 $M_{\odot}$
protostar. However, we cannot explain the observed low luminosity with the
standard pre-main-sequence evolutionary track unless we assume cold accretion
with an extremely small initial radius of the protostar ($\sim$0.65 $R_\odot$).
These facts may challenge our current understanding of the low mass star
formation, in particular the mass accretion process onto the protostar and the
circumstellar disk.
