We present SMA CO(2-1) observations toward the protostellar jet driven by SVS13A, a variable protostar in the NGC1333 star-forming region. The SMA CO(2-1) images show an extremely high-velocity jet composed of a series of molecular bullets. Based on the SMA CO observations, we discover clear and large systematic velocity gradients, perpendicular to the jet axis, in the blueshifted and redshifted bullets. After discussing several alternative interpretations, such as twin-jets, jet precession, warped disk, and internal helical shock, we suggest that the systematic velocity gradients observed in the bullets result from the rotation of the SVS13A jet. From the SMA CO images, the measured rotation velocities are 11.7-13.7 km/s for the blueshifted bullet and 4.7+/-0.5 km/s for the redshifted bullet. The estimated specific angular momenta of the two bullets are comparable to those of dense cores, about 10 times larger than those of protostellar envelopes, and about 20 times larger than those of circumstellar disks. If the velocity gradients are due to the rotation of the SVS13A jet, the significant amount of specific angular momenta of the bullets indicates that the rotation of jets/outflows is a key mechanism to resolve the so-called angular momentum problem in the field of star formation. The kinematics of the bullets suggests that the jet launching footprint on the disk has a radius of about 7.2-7.7 au, which appears to support the extended disk-wind model. We note that further observations are needed to comprehensively understand the kinematics of the SVS13A jet, in order to confirm the rotation nature of the bullets.
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