We have studied the physical and chemical properties of a quiescent starless core L1521E with various molecular lines. We found that there exists a compact dense core traced by the H¹³CO⁺, HN¹³C, CCS, and HC₃N lines; their distributions have a single peak at the same position. The core radius is as small as 0.031 pc, whereas the H₂ density at the peak position is as high as (1.3-5.6) × 10⁵ cm^-3. Although the density is high enough to excite the inversion transitions of NH₃, these lines are found to be very faint in L1521E. The distributions of NH₃ and CCS seem to be different from those of well-studied starless cores, L1498 and L1544, where the distribution of CCS shows a shell-like structure, while that of NH₃ is concentrated at the center of the core. Abundances of carbon-chain molecules are higher in L1521E than in the other dark cloud cores; in particular, those of sulfur-bearing molecules C_nS are comparable to the cyanopolyyne peak of TMC-1. Our results suggest that L1521E would be in a very early stage of physical and chemical evolution.