We imaged two starless molecular cloud cores, TUKH083 and TUKH122, in the Orion A giant molecular cloud in the CCS and ammonia (NH$_3$) emission with the Very Large Array. TUKH122 contains one NH$_3$ core TUKH122-n, which is elongated and has a smooth oval boundary. Where observed, the CCS emission surrounds the NH$_3$ core. This configuration resembles that of the N$_2$H$^+$ and CCS distribution in the Taurus starless core L1544, a well-studied example of a dense prestellar core exhibiting infall motions. The linewidth of TUKH122-n is narrow (0.20 km s$^{-1}$) in the NH$_3$ emission line and therefore dominated by thermal motions. The smooth oval shape of the core boundary and narrow linewidth in NH$_3$ seem to imply that TUKH122-n is dynamically relaxed and quiescent. TUKH122-n is similar to L1544 in the kinetic temperature (10 K), linear size (0.03 pc), and virial mass ($sim$ 2 $M_{odot}$). Our results strongly suggest that TUKH122-n is on the verge of star formation. TUKH122-n is embedded in the 0.2 pc massive (virial mass $sim$ 30 $M_{odot}$) turbulent parent core, while the L1544 NH$_3$ core is embedded in the 0.2 pc less-massive (virial mass $sim$ 10 $M_{odot}$) thermal parent core. TUKH083 shows complicated distribution in NH$_3$, but was not detected in CCS. The CCS emission toward TUKH083 appears to be extended, and is resolved out in our interferometric observations.