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Context. Rotationally supported disks are critical in the star formation process. The questions of when they form and what factors influence or hinder their formation have been studied but are largely unanswered. Observations of early-stage YSOs are needed to probe disk formation. Aims. VLA1623 is a triple non-coeval protostellar system, with a weak magnetic field perpendicular to the outflow, whose Class 0 component, VLA1623A, shows a disk-like structure in continuum with signatures of rotation in line emission. We aim to determine whether this structure is in part or in whole a rotationally supported disk, i.e. a Keplerian disk, and what its characteristics are. Methods. ALMA Cycle 0 Early Science 1.3 mm continuum and C 18 O (2-1) observations in the extended configuration are presented here and used to perform an analysis of the disk-like structure using position-velocity (PV) diagrams and thin disk modeling with the addition of foreground absorption. Results. The PV diagrams of the C 18 O line emission suggest the presence of a rotationally supported component with a radius of at least 50 AU. Kinematical modeling of the line emission shows that the disk out to 180 AU is actually rotationally supported, with the rotation described well by Keplerian rotation out to at least 150 AU, and the central source mass is 0.2 M for an inclination of 55 . Pure infall and conserved angular momentum rotation models are excluded. Conclusions. VLA1623A, a very young Class 0 source, presents a disk with an outer radius R out = 180 AU with a Keplerian velocity structure out to at least 150 AU. The weak magnetic fields and recent fragmentation in this region of Ophiuchus may have played a leading role in the formation of the disk.