We report ALMA observations in 0.87 mm continuum and <SUP>12</SUP>CO (J = 3-2) toward a very low-luminosity (<0.1 L <SUB>☉</SUB>) protostar, which is deeply embedded in one of the densest cores, MC27/L1521F, in Taurus with an indication of multiple star formation in a highly dynamical environment. The beam size corresponds to ̃20 au, and we have clearly detected blueshifted/redshifted gas in <SUP>12</SUP>CO associated with the protostar. The spatial/velocity distributions of the gas show there is a rotating disk with a size scale of ̃10 au, a disk mass of ̃10<SUP>-4</SUP> M <SUB>☉</SUB>, and a central stellar mass of ̃0.2 M <SUB>☉</SUB>. 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 ̃10<SUP>6</SUP> cm<SUP>-3</SUP>. 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 ̃0.2 M <SUB>☉</SUB> 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 (̃0.65 {R}<SUB>☉ </SUB>). 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....