We have made synthesis imaging of a starless core in the Taurus molecular cloud L1521F, with two key chemical evolutionary tracers, CCS (J_N = 3_2 - 2_1), which traces young evolutionary phase of cores, and N_2H~+ (J=1-0), which traces until the late evolutionary phase, as well as mapping observations of submillimeter dust continuum. The peak positions, as well as the radial distributions, of N_2H~+ and dust continuum coincide with each other. Unlike the other tracers, CCS shows a dip at the dust continuum center, suggesting that the abundance of the molecule decreases at the core center because of depletion and chemical reactions. The channel maps of both molecular lines clearly revealed clumpy substructures inside the core. Using an automatic and objective routine, eight and four clumps have been identified in the CCS and N_2H~+ channel maps, respectively. The abundances of the molecules are estimated toward the dust continuum center. Using our derived abundances, the LTE masses for each clump are estimated. The CCS components, which appear to trace the envelope, show an overall velocity gradient from east to west, whereas a N_2H~+ clump located at the core center shows a gradient from west to east. Assuming that the velocity gradients are due to rotation, the observational results indicate that the rotation of the outer envelope (size approx<0.08 pc ～ 16, 000 AU) and that of the central compact region (size approx<0.03 pc ～ 6000 AU) have different axes with almost opposite senses of rotation. The velocity gradients of the southern and northern CCS components are estimated to be 7.2 and 9.2 km s~(-1) pc~(-1) at size scales of 0.05 and 0.04 pc, respectively. The velocity gradient of the N_2H~+ components at the core center is estimated to be 15 km s~(-1) pc~(-1) at a size scale of 0.01 pc (～2000 AU). Examining the line width-size correlation of these clumps and of other cold (kinetic temperature T_K approx< 10 K) starless cores, the slope index is found to be slightly shallower than those values for cores containing stars. Assuming a spherical, homogeneous sphere, the ratios of rotational to gravitational energy, β, of these cores are calculated to be ～0.3 for the CCS and ～1.0 for the N_2H~+ components, respectively. The relation of the specific angular momentum (J/M) to size seen at scales larger than ～0.03 pc (～6000 AU) appears to flatten out at sizes smaller than ～ 6000 AU, for which the specific angular momentum is relatively constant at ～0.002. This is consistent with results reported by Ohashi et al. Based on a chemical evolutionary model, the core may be in a young starless cores phase, assuming that the dip of CCS at the core center is caused by depletion and chemical reaction. L1521F may be in a younger starless-core phase than L1544.
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